Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 6 - Two Dimensional Analytical Geometry [Latest edition]

## Chapter 6: Two Dimensional Analytical Geometry

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4Exercise 6.5
Exercise 6.1 [Pages 243 - 244]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 6 Two Dimensional Analytical GeometryExercise 6.1 [Pages 243 - 244]

Exercise 6.1 | Q 1. (i) | Page 243

Find the locus of P, if for all values of α, the co-ordinates of a moving point P is (9 cos α, 9 sin α)

Exercise 6.1 | Q 1. (ii) | Page 243

Find the locus of P, if for all values of α, the co-ordinates of a moving point P is (9 cos α, 6 sin α)

Exercise 6.1 | Q 2. (i) | Page 243

Find the locus of a point P that moves at a constant distant of two units from the x-axis

Exercise 6.1 | Q 2. (ii) | Page 243

Find the locus of a point P that moves at a constant distant of three units from the y-axis

Exercise 6.1 | Q 3 | Page 243

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x = a cos3θ, y = a sin3θ

Exercise 6.1 | Q 4 | Page 243

Find the value of k and b, if the points P(−3, 1) and Q(2, b) lie on the locus of x2 − 5x + ky = 0

Exercise 6.1 | Q 5 | Page 243

A straight rod of length 8 units slides with its ends A and B always on the x and y axes respectively. Find the locus of the midpoint of the line segment AB

Exercise 6.1 | Q 6 | Page 243

Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3, 5), (1, −1) is equal to 20

Exercise 6.1 | Q 7 | Page 243

Find the equation of the locus of the point P such that the line segment AB, joining the points A(1, −6) and B(4, −2), subtends a right angle at P

Exercise 6.1 | Q 8 | Page 243

If O is origin and R is a variable point on y2 = 4x, then find the equation of the locus of the mid-point of segment OR

Exercise 6.1 | Q 9 | Page 243

The coordinates of a moving point P are ("a"/2 ("cosec" theta + sin theta), "b"/2 ("cosec" theta - sin theta)) where θ is a variabe parameter. Show hat the equation of the locus P is b2x2 – a2y2 = a2b2

Exercise 6.1 | Q 10 | Page 243

If P(2, – 7) is given point and Q is a point on 2x2 + 9y2 = 18 then find the equations of the locus of the midpoint of PQ

Exercise 6.1 | Q 11 | Page 244

If R is any point on the x-axis and Q is any point on the y-axis and P is a variable point on RQ with RP = b, PQ = a. then find the equation of locus of P

Exercise 6.1 | Q 12 | Page 244

If the points P(6, 2) and Q(– 2, 1) and R are the vertices of a ∆PQR and R is the point on the locus y = x2 – 3x + 4, then find the equation of the locus of centroid of ∆PQR

Exercise 6.1 | Q 13 | Page 244

If Q is a point on the locus of x2 + y2 + 4x – 3y +7 = 0, then find the equation of locus of P which divides segment OQ externally in the ratio 3 : 4 where O is origin

Exercise 6.1 | Q 14 | Page 244

Find the points on the locus of points that are 3 units from x-axis and 5 units from the point (5, 1)

Exercise 6.1 | Q 15 | Page 244

The sum of the distance of a moving point from the points (4, 0) and (−4, 0) is always 10 units. Find the equation of the locus of the moving point

Exercise 6.2 [Pages 260 - 261]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 6 Two Dimensional Analytical GeometryExercise 6.2 [Pages 260 - 261]

Exercise 6.2 | Q 1. (i) | Page 260

Find the equation of the lines passing through the point (1, 1) with y-intercept (– 4)

Exercise 6.2 | Q 1. (ii) | Page 260

Find the equation of the lines passing through the point (1,1) with slope 3

Exercise 6.2 | Q 1. (iii) | Page 260

Find the equation of the lines passing through the point (1,1) and (– 2, 3)

Exercise 6.2 | Q 1. (iv) | Page 260

Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis

Exercise 6.2 | Q 2 | Page 260

If P(r, c) is midpoint of a line segment between the axes then show that x/"r" + y/"c" = 2

Exercise 6.2 | Q 3 | Page 260

Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10

Exercise 6.2 | Q 4 | Page 260

If p is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that 1/("p"^3) = 1/("a"^2) + 1/("b"^2)

Exercise 6.2 | Q 5. (i) | Page 260

The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the linear relationship between C and F

Exercise 6.2 | Q 5. (ii) | Page 260

The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of C for 98.6°F

Exercise 6.2 | Q 5. (iii) | Page 260

The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the value of F for 38°C

Exercise 6.2 | Q 6. (i) | Page 260

An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance between the place and the target

Exercise 6.2 | Q 6. (ii) | Page 260

An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance covered by it in 15 seconds

Exercise 6.2 | Q 6. (iii) | Page 260

An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find time taken to hit the target

Exercise 6.2 | Q 7 | Page 260

Population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant)

Exercise 6.2 | Q 8 | Page 260

Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12

Exercise 6.2 | Q 9 | Page 260

Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1

Exercise 6.2 | Q 10. (i) | Page 260

Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by using concept of slope

Exercise 6.2 | Q 10. (ii) | Page 260

Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by using a straight line

Exercise 6.2 | Q 10. (iii) | Page 260

Show that the points (1, 3), (2, 1) and (1/2, 4) are collinear, by using any other method

Exercise 6.2 | Q 11 | Page 260

A straight line is passing through the point A(1, 2) with slope 5/12. Find points on the line which are 13 units away from A

Exercise 6.2 | Q 12. (i) | Page 260

A 150 m long train is moving with constant velocity of 12.5 m/s. Find the equation of the motion of the train

Exercise 6.2 | Q 12. (ii) | Page 260

A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole

Exercise 6.2 | Q 12. (iii) | Page 260

A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross the bridge of length 850 m

Exercise 6.2 | Q 13. (i) | Page 260

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

 Weight (kg) 2 4 5 8 Length (cm) 3 4 4.5 6

Draw a graph showing the results.

Exercise 6.2 | Q 13. (ii) | Page 260

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

 Weight (kg) 2 4 5 8 Length (cm) 3 4 4.5 6

Find the equation relating the length of the spring to the weight on it

Exercise 6.2 | Q 13. (iii) | Page 260

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

 Weight (kg) 2 4 5 8 Length (cm) 3 4 4.5 6

What is the actual length of the spring

Exercise 6.2 | Q 13. (iv) | Page 260

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

 Weight (kg) 2 4 5 8 Length (cm) 3 4 4.5 6

If the spring has to stretch to 9 cm long, how much weight should be added?

Exercise 6.2 | Q 13. (v) | Page 260

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

 Weight (kg) 2 4 5 8 Length (cm) 3 4 4.5 6

How long will the spring be when 6 kilograms of weight on it?

Exercise 6.2 | Q 14. (i) | Page 261

A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days

Exercise 6.2 | Q 14. (ii) | Page 261

A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Draw the graph for first 96days

Exercise 6.2 | Q 15. (i) | Page 261

In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the minimum total length of the escalator

Exercise 6.2 | Q 15. (ii) | Page 261

In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction

Exercise 6.2 | Q 15. (iii) | Page 261

In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the slopes of the escalator at the turning points

Exercise 6.3 [Pages 271 - 272]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 6 Two Dimensional Analytical GeometryExercise 6.3 [Pages 271 - 272]

Exercise 6.3 | Q 1 | Page 271

Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines

Exercise 6.3 | Q 2 | Page 271

Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3

Exercise 6.3 | Q 3. (i) | Page 271

Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)

Exercise 6.3 | Q 3. (ii) | Page 271

Find the distance between the line 4x + 3y + 4 = 0, and a point (7, −3)

Exercise 6.3 | Q 4. (i) | Page 271

Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0

Exercise 6.3 | Q 4. (ii) | Page 271

Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6

Exercise 6.3 | Q 5 | Page 271

If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal

Exercise 6.3 | Q 6. (i) | Page 271

Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and through the point (−1, 2)

Exercise 6.3 | Q 6. (ii) | Page 271

Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and parallel to x − y + 5 = 0

Exercise 6.3 | Q 6. (iii) | Page 271

Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and perpendicular to x − 2y + 1 = 0

Exercise 6.3 | Q 7 | Page 271

Find the equations of two straight lines which are parallel to the line 12x + 5y + 2 = 0 and at a unit distance from the point (1, −1)

Exercise 6.3 | Q 8 | Page 271

Find the equations of straight lines which are perpendicular to the line 3x + 4y − 6 = 0 and are at a distance of 4 units from (2, 1)

Exercise 6.3 | Q 9 | Page 271

Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15

Exercise 6.3 | Q 10 | Page 272

Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0

Exercise 6.3 | Q 11 | Page 272

If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a

Exercise 6.3 | Q 12. (i) | Page 272

Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0

Exercise 6.3 | Q 12. (ii) | Page 272

Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0

Exercise 6.3 | Q 13. (i) | Page 272

Find the family of straight lines perpendicular

Exercise 6.3 | Q 13. (ii) | Page 272

Find the family of straight lines parallel to 3x + 4y – 12

Exercise 6.3 | Q 14 | Page 272

If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position

Exercise 6.3 | Q 15 | Page 272

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A

Exercise 6.3 | Q 16 | Page 272

A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units

Exercise 6.3 | Q 17 | Page 272

Find the image of the point (−2, 3) about the line x + 2y − 9 = 0

Exercise 6.3 | Q 18. (i) | Page 272

A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Draw graph of the cost as x goes from 0 to 50 copies

Exercise 6.3 | Q 18. (ii) | Page 272

A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Find the cost of making 40 copies

Exercise 6.3 | Q 19 | Page 272

Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers

Exercise 6.3 | Q 20 | Page 272

Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers

Exercise 6.4 [Pages 281 - 282]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 6 Two Dimensional Analytical GeometryExercise 6.4 [Pages 281 - 282]

Exercise 6.4 | Q 1 | Page 281

Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0

Exercise 6.4 | Q 2 | Page 281

Show that 4x2 + 4xy + y2 − 6x − 3y − 4 = 0 represents a pair of parallel lines

Exercise 6.4 | Q 3 | Page 281

Show that 2x2 + 3xy − 2y2 + 3x + y + 1 = 0 represents a pair of perpendicular lines

Exercise 6.4 | Q 4 | Page 281

Show that the equation 2x2 − xy − 3y2 − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan−1(5)

Exercise 6.4 | Q 5 | Page 281

Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x2 – 2xy sec 2α + y2 = 0

Exercise 6.4 | Q 6 | Page 281

Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y + 1 = 0 and 5x + y − 3 = 0

Exercise 6.4 | Q 7. (i) | Page 282

Find the separate equation of the following pair of straight lines
3x2 + 2xy – y2 = 0

Exercise 6.4 | Q 7. (ii) | Page 282

Find the separate equation of the following pair of straight lines
6(x – 1)2 + 5(x – 1)(y – 2) – 4(y – 3)2 = 0

Exercise 6.4 | Q 7. (iii) | Page 282

Find the separate equation of the following pair of straight lines
2x2 – xy – 3y2 – 6x + 19y – 20 = 0

Exercise 6.4 | Q 8 | Page 282

The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is twice that of the other, show that 8h2 = 9ab

Exercise 6.4 | Q 9 | Page 282

The slope of one of the straight lines ax2 + 2hxy + by2 = 0 is three times the other, show that 3h2 = 4ab

Exercise 6.4 | Q 10 | Page 282

A ∆OPQ is formed by the pair of straight lines x2 – 4xy + y2 = 0 and the line PQ. The equation of PQ is x + y – 2 = 0, Find the equation of the median of the triangle ∆ OPQ drawn from the origin O

Exercise 6.4 | Q 11 | Page 282

Find p and q, if the following equation represents a pair of perpendicular lines
6x2 + 5xy – py2 + 7x + qy – 5 = 0

Exercise 6.4 | Q 12 | Page 282

Find the value of k, if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting, 12x2 + 7xy − 12y2 − x + 7y + k = 0

Exercise 6.4 | Q 13 | Page 282

For what values of k does the equation 12x2 + 2kxy + 2y2 +11x – 5y + 2 = 0 represent two straight lines

Exercise 6.4 | Q 14 | Page 282

Show that the equation 9x2 – 24xy + 16y2 – 12x + 16y – 12 = 0 represents a pair of parallel lines. Find the distance between them

Exercise 6.4 | Q 15 | Page 282

Show that the equation 4x2 + 4xy + y2 – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them

Exercise 6.4 | Q 16 | Page 282

Prove that one of the straight lines given by ax2 + 2hxy + by2 = 0 will bisect the angle between the coordinate axes if (a + b)2 = 4h2

Exercise 6.4 | Q 17 | Page 282

If the pair of straight lines x2 – 2kxy – y2 = 0 bisect the angle between the pair of straight lines x2 – 2lxy – y2 = 0, Show that the later pair also bisects the angle between the former

Exercise 6.4 | Q 18 | Page 282

Prove that the straight lines joining the origin to the points of intersection of 3x2 + 5xy – 3y2 + 2x + 3y = 0 and 3x – 2y – 1 = 0 are at right angles

Exercise 6.5 [Pages 282 - 284]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 6 Two Dimensional Analytical GeometryExercise 6.5 [Pages 282 - 284]

#### MCQ

Exercise 6.5 | Q 1 | Page 282

Choose the correct alternative:
The equation of the locus of the point whose distance from y-axis is half the distance from origin is

• x2 + 3y2 = 0

• x2 – 3y2 = 0

• 3x + y2 = 0

• 3x2 – y2 = 0

Exercise 6.5 | Q 2 | Page 282

Choose the correct alternative:
Which of the following equation is the locus of (at2, 2at)

• x^2/"a"^2 - y^2/"b"^2 = 1

• x^2/"a"^2 + y^2/"b"^2 = 1

• x2 + y2 = a2

• y2 = 4ax

Exercise 6.5 | Q 3 | Page 282

Choose the correct alternative:
Which of the following point lie on the locus of 3x2 + 3y2 – 8x – 12y + 17 = 0

• (0, 0)

• (−2, 3)

• (1, 2)

• (0, −1)

Exercise 6.5 | Q 4 | Page 282

Choose the correct alternative:
If the point (8,−5) lies on the locus x^2/1 - y^2/25 = k, then the value of k is

• 0

• 1

• 2

• 3

Exercise 6.5 | Q 5 | Page 283

Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if

• α + 2β = 7

• 3α + β = 9

• α + 3β = 11

• 3α + β = 11

Exercise 6.5 | Q 6 | Page 283

Choose the correct alternative:
The slope of the line which makes an angle 45° with the line 3x − y = −5 are

• 1, −1

• 1/2, - 2

• 1, 1/2

• 2, - 1/2

Exercise 6.5 | Q 7 | Page 283

Choose the correct alternative:
Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2sqrt(2) is

• x + y + 2 = 0

• x + y − 2 = 0

• x + y - sqrt(2) = 0

• x + y + sqrt(2) = 0

Exercise 6.5 | Q 8 | Page 283

Choose the correct alternative:
The coordinates of the four vertices of a quadrilateral are (−2, 4), (−1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (−1, 2) and dividing the quadrilateral in the equal areas is

• x + 1 = 0

• x + y = 1

• x + y + 3 = 0

• x − y + 3 = 0

Exercise 6.5 | Q 9 | Page 283

Choose the correct alternative:
The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

• 5, −5

• 5, 5

• 5, 3

• 5, −4

Exercise 6.5 | Q 10 | Page 283

Choose the correct alternative:
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to sqrt(5) is

• x - 2y = sqrt(5)

• 2x - y = sqrt(5)

• 2x − y + 5 = 0

• x − 2y − 5 = 0

Exercise 6.5 | Q 11 | Page 283

Choose the correct alternative:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is

• x + 5y +- 5sqrt(2) = 0

• x - 5y +- 5sqrt(2) = 0

• 5x + y +- 5sqrt(2) = 0

• 5x - y +- 5sqrt(2) = 0

Exercise 6.5 | Q 12 | Page 283

Choose the correct alternative:
Equation of the straight line perpendicular to the line x − y + 5 = 0, through the point of intersection the y-axis and the given line

• x − y − 5 = 0

• x + y − 5 = 0

• x + y + 5 = 0

• x + y + 10 = 0

Exercise 6.5 | Q 13 | Page 283

Choose the correct alternative:
If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is

• sqrt(3/2)

• 6

• sqrt(6)

• 3sqrt(2)

Exercise 6.5 | Q 14 | Page 283

Choose the correct alternative:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point

• (3/2, 5/2)

• (2/5, 2/5)

• (3/5, 3/5)

• (2/5, 3/5)

Exercise 6.5 | Q 15 | Page 283

Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is

• (7, 3)

• (4, 1)

• (1, −1)

• (−2, 3)

Exercise 6.5 | Q 16 | Page 283

Choose the correct alternative:
The image of the point (2, 3) in the line y = −x is

• (−3, −2)

• (−3, 2)

• (−2, −3)

• (3, 2)

Exercise 6.5 | Q 17 | Page 283

Choose the correct alternative:
The length of ⊥ from the origin to the line x/3 - y/4 = 1 is

• 11/5

• 5/12

• 12/5

• - 5/12

Exercise 6.5 | Q 18 | Page 283

Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is

• 3/2

• 9/2

• 2/3

• 2/9

Exercise 6.5 | Q 19 | Page 284

Choose the correct alternative:
If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is

• k = 3

• k = 1/3

• k = 2/3

• k = 3/2

Exercise 6.5 | Q 20 | Page 284

Choose the correct alternative:
If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is

• 20 sq.units

• 16 sq.units

• 25 sq.units

• 4 sq.units

Exercise 6.5 | Q 21 | Page 284

Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =

• - 6/7

• 6/7

• - 7/6

• 7/6

Exercise 6.5 | Q 22 | Page 284

Choose the correct alternative:
The area of the triangle formed by the lines x– 4y2 = 0 and x = a is

• 2a2

• sqrt(3)/2 "a"^2

• 1/2 "a"^2

• 2/sqrt(3) "a"^2

Exercise 6.5 | Q 23 | Page 284

Choose the correct alternative:
If one of the lines given by 6x2 – xy – 4cy2 = 0 is 3x + 4y = 0, then c equals to

• −3

• −1

• 3

• 1

Exercise 6.5 | Q 24 | Page 284

Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then (2costheta + 3sintheta)/(4costheta + 5costheta)

• 1

• - 1/9

• 5/9

• 1/9

Exercise 6.5 | Q 25 | Page 284

Choose the correct alternative:
One of the equation of the lines given by x2 + 2xy cot θ – y2 = 0 is

• x − y cot θ = 0

• x + y tan θ = 0

• x cos θ + y(sin θ + 1) = 0

• x sin θ + y(cos θ + 1) = 0

## Chapter 6: Two Dimensional Analytical Geometry

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4Exercise 6.5

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 6 - Two Dimensional Analytical Geometry

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 6 (Two Dimensional Analytical Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 11th Mathematics Volume 1 and 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 6 Two Dimensional Analytical Geometry are Introduction to Two Dimensional Analytical Geometry, Locus of a Point, Straight Lines, Angle Between Two Straight Lines, Pair of Straight Lines.

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