Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 3 - Analytical Geometry [Latest edition]

## Chapter 3: Analytical Geometry

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Exercise 3.5Exercise 3.6Exercise 3.7Miscellaneous Problems
Exercise 3.1 [Page 53]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.1 [Page 53]

Exercise 3.1 | Q 1 | Page 53

Find the locus of a point which is equidistant from (1, 3) and x axis.

Exercise 3.1 | Q 2 | Page 53

A point moves so that it is always at a distance of 4 units from the point (3, –2)

Exercise 3.1 | Q 3 | Page 53

If the distance of a point from the points (2, 1) and (1, 2) are in the ratio 2 :1, then find the locus of the point.

Exercise 3.1 | Q 4 | Page 53

Find a point on x axis which is equidistant from the points (7, –6) and (3, 4).

Exercise 3.1 | Q 5 | Page 53

If A(-1, 1) and B(2, 3) are two fixed points, then find the locus of a point P so that the area of triangle APB = 8 sq.units.

Exercise 3.2 [Page 57]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.2 [Page 57]

Exercise 3.2 | Q 1 | Page 57

Find the angle between the lines whose slopes are 1/2 and 3.

Exercise 3.2 | Q 2 | Page 57

Find the distance of the point (4, 1) from the line 3x – 4y + 12 = 0.

Exercise 3.2 | Q 3 | Page 57

Show that the straight lines x + y – 4 = 0, 3x + 2 = 0 and 3x – 3y + 16 = 0 are concurrent.

Exercise 3.2 | Q 4 | Page 57

Find the value of ‘a’ for which the straight lines 3x + 4y = 13; 2x – 7y = -1 and ax – y – 14 = 0 are concurrent.

Exercise 3.2 | Q 5 | Page 57

A manufacturer produces 80 TV sets at a cost of ₹ 2,20,000 and 125 TV sets at a cost of ₹ 2,87,500. Assuming the cost curve to be linear, find the linear expression of the given information. Also, estimate the cost of 95 TV sets.

Exercise 3.3 [Page 60]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.3 [Page 60]

Exercise 3.3 | Q 1 | Page 60

If the equation ax2 + 5xy – 6y2 + 12x + 5y + c = 0 represents a pair of perpendicular straight lines, find a and c.

Exercise 3.3 | Q 2 | Page 60

Show that the equation 12x2 – 10xy + 2y2 + 14x – 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.

Exercise 3.3 | Q 3 | Page 60

Show that the pair of straight lines 4x2 + 12xy + 9y2 – 6x – 9y + 2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines.

Exercise 3.3 | Q 4 | Page 60

Find the angle between the pair of straight lines 3x2 – 5xy – 2y2 + 17x + y + 10 = 0.

Exercise 3.4 [Page 64]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.4 [Page 64]

Exercise 3.4 | Q 1. (i) | Page 64

Find the equation of the following circles having the centre (3, 5) and radius 5 units.

Exercise 3.4 | Q 1. (ii) | Page 64

Find the equation of the following circles having the centre (0,0) and radius 2 units

Exercise 3.4 | Q 2. (i) | Page 64

Find the centre and radius of the circle

x2 + y2 = 16

Exercise 3.4 | Q 2. (ii) | Page 64

Find the centre and radius of the circle

x2 + y2 – 22x – 4y + 25 = 0

Exercise 3.4 | Q 2. (iii) | Page 64

Find the centre and radius of the circle.

5x2 + 5y2+ 4x – 8y – 16 = 0

Exercise 3.4 | Q 2. (iv) | Page 64

Find the centre and radius of the circle.

(x + 2) (x – 5) + (y – 2) (y – 1) = 0

Exercise 3.4 | Q 3 | Page 64

Find the equation of the circle whose centre is (-3, -2) and having circumference 16π.

Exercise 3.4 | Q 4 | Page 64

Find the equation of the circle whose centre is (2, 3) and which passes through (1, 4).

Exercise 3.4 | Q 5 | Page 64

Find the equation of the circle passing through the points (0, 1), (4, 3) and (1, -1).

Exercise 3.4 | Q 6 | Page 64

Find the equation of the circle on the line joining the points (1, 0), (0, 1), and having its centre on the line x + y = 1.

Exercise 3.4 | Q 7 | Page 64

If the lines x + y = 6 and x + 2y = 4 are diameters of the circle, and the circle passes through the point (2, 6) then find its equation.

Exercise 3.4 | Q 8 | Page 64

Find the equation of the circle having (4, 7) and (-2, 5) as the extremities of a diameter.

Exercise 3.4 | Q 9 | Page 64

Find the Cartesian equation of the circle whose parametric equations are x = 3 cos θ, y = 3 sin θ, 0 ≤ θ ≤ 2π.

Exercise 3.5 [Page 66]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.5 [Page 66]

Exercise 3.5 | Q 1 | Page 66

Find the equation of the tangent to the circle x2 + y2 – 4x + 4y – 8 = 0 at (-2, -2).

Exercise 3.5 | Q 2 | Page 66

Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x2 + y2 – 4x – 6y + 9 = 0.

Exercise 3.5 | Q 3 | Page 66

Find the length of the tangent from (1, 2) to the circle x2 + y2 – 2x + 4y + 9 = 0.

Exercise 3.5 | Q 4 | Page 66

Find the value of P if the line 3x + 4y – P = 0 is a tangent to the circle x2 + y2 = 16.

Exercise 3.6 [Pages 70 - 71]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.6 [Pages 70 - 71]

Exercise 3.6 | Q 1 | Page 70

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.

Exercise 3.6 | Q 2 | Page 71

The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.

Exercise 3.6 | Q 3 | Page 71

Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.

Exercise 3.6 | Q 4. (a) | Page 71

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

y2 = 20x

Exercise 3.6 | Q 4. (b) | Page 71

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x2 = 8y

Exercise 3.6 | Q 4. (c) | Page 71

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x2 = - 16y

Exercise 3.6 | Q 5 | Page 71

The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ 1/5x2 – 6x + 100. Show that the average variable cost curve is a parabola. Also, find the output and the average cost at the vertex of the parabola.

Exercise 3.6 | Q 6 | Page 71

The profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.

Exercise 3.7 [Pages 71 - 73]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryExercise 3.7 [Pages 71 - 73]

Exercise 3.7 | Q 1 | Page 71

If m1 and m2 are the slopes of the pair of lines given by ax2 + 2hxy + by2 = 0, then the value of m1 + m2 is:

• (2"h")/"b"

• -(2"h")/"b"

• (2"h")/"a"

• -(2"h")/"a"

Exercise 3.7 | Q 2 | Page 71

The angle between the pair of straight lines x2 – 7xy + 4y2 = 0 is:

• tan^-1 (1/3)

• tan^-1 (1/2)

• tan^-1 (sqrt33/5)

• tan^-1 (5/sqrt33)

Exercise 3.7 | Q 3 | Page 71

If the lines 2x – 3y – 5 = 0 and 3x – 4y – 7 = 0 are the diameters of a circle, then its centre is:

• (-1, 1)

• (1, 1)

• (1, -1)

• (-1, -1)

Exercise 3.7 | Q 4 | Page 71

The x-intercept of the straight line 3x + 2y – 1 = 0 is

• 3

• 2

• 1/3

• 1/2

Exercise 3.7 | Q 5 | Page 71

The slope of the line 7x + 5y – 8 = 0 is:

• 7/5

• -7/5

• 5/7

• -5/7

Exercise 3.7 | Q 6 | Page 71

The locus of the point P which moves such that P is at equidistance from their coordinate axes is:

• y = 1/x

• y = - x

• y = x

• y = (-1)/x

Exercise 3.7 | Q 7 | Page 71

The locus of the point P which moves such that P is always at equidistance from the line x + 2y + 7 = 0:

• x + 2y + 2 = 0

• x – 2y + 1 = 0

• 2x – y + 2 = 0

• 3x + y + 1 = 0

Exercise 3.7 | Q 8 | Page 71

If kx2 + 3xy – 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to:

• 1/2

• -1/2

• 2

• - 2

Exercise 3.7 | Q 9 | Page 71

(1, -2) is the centre of the circle x2 + y2 + ax + by – 4 = 0, then its radius:

• 3

• 2

• 4

• 1

Exercise 3.7 | Q 10 | Page 71

The length of the tangent from (4, 5) to the circle x2 + y2 = 16 is:

• 4

• 5

• 16

• 25

Exercise 3.7 | Q 11 | Page 71

The focus of the parabola x2 = 16y is:

• (4 , 0)

• (-4 , 0)

• (0, 4)

• (0, - 4)

Exercise 3.7 | Q 12 | Page 72

Length of the latus rectum of the parabola y2 = -25x:

• 25

• -5

• 5

• -25

Exercise 3.7 | Q 13 | Page 72

The centre of the circle x2 + y2 – 2x + 2y – 9 = 0 is:

• (1, 1)

• (-1, 1)

• (-1, 1)

• (1, -1)

Exercise 3.7 | Q 14 | Page 72

The equation of the circle with centre on the x axis and passing through the origin is:

• x2 – 2ax + y2 = 0

• y2 – 2ay + x2 = 0

• x2 + y2 = a2

• x2 – 2ay + y2 = 0

Exercise 3.7 | Q 15 | Page 72

If the centre of the circle is (-a, -b) and radius is sqrt("a"^2 - "b"^2) then the equation of circle is:

• x2 + y2 + 2ax + 2by + 2b2 = 0

• x2 + y2 + 2ax + 2by – 2b2 = 0

• x2 + y2 – 2ax – 2by – 2b2 = 0

• x2 + y2 – 2ax – 2by + 2b2 = 0

Exercise 3.7 | Q 16 | Page 72

Combined equation of co-ordinate axes is:

• x2 – y2 = 0

• x2 + y2 = 0

• xy = c

• xy = 0

Exercise 3.7 | Q 17 | Page 72

ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then ‘a’ is:

• 2

• -2

• 4

• -4

Exercise 3.7 | Q 18 | Page 72

In the equation of the circle x2 + y2 = 16 then v intercept is (are):

• 4

• 16

• ± 4

• ± 16

Exercise 3.7 | Q 19 | Page 72

If the perimeter of the circle is 8π units and centre is (2, 2) then the equation of the circle is:

• (x – 2)2 + (y – 2)2 = 4

• (x – 2)2 + (y – 2)2 = 16

• (x – 4)2 + (y – 4)2 = 16

• x2 + y2 = 4

Exercise 3.7 | Q 20 | Page 72

The equation of the circle with centre (3, -4) and touches the x-axis is:

• (x – 3)2 + (y – 4)2 = 4

• (x – 3)2 + (y + 4)2 = 16

• (x – 3)2 + (y – 4)2 = 16

• x2 + y2 = 16

Exercise 3.7 | Q 21 | Page 72

If the circle touches the x-axis, y-axis, and the line x = 6 then the length of the diameter of the circle is:

• 6

• 3

• 12

• 4

Exercise 3.7 | Q 22 | Page 72

The eccentricity of the parabola is:

• 3

• 2

• 0

• 1

Exercise 3.7 | Q 23 | Page 72

The double ordinate passing through the focus is:

• focal chord

• latus rectum

• directrix

• axis

Exercise 3.7 | Q 24 | Page 72

The distance between directrix and focus of a parabola y2 = 4ax is:

• a

• 2a

• 4a

• 3a

Exercise 3.7 | Q 25 | Page 73

The equation of directrix of the parabola y2 = -x is:

• 4x + 1 = 0

• 4x - 1 = 0

• x – 1 = 0

• x + 4 = 0

Miscellaneous Problems [Page 73]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 3 Analytical GeometryMiscellaneous Problems [Page 73]

Miscellaneous Problems | Q 1 | Page 73

A point P moves so that P and the points (2, 2) and (1, 5) are always collinear. Find the locus of P.

Miscellaneous Problems | Q 2 | Page 73

As the number of units produced increases from 500 to 1000 and the total cost of production increases from ₹ 6000 to ₹ 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear.

Miscellaneous Problems | Q 3 | Page 73

Prove that the lines 4x + 3y = 10, 3x - 4y = - 5 and 5x + y = 7 are concurrent.

Miscellaneous Problems | Q 4 | Page 73

Find the value of p for which the straight lines 8px + (2 - 3p)y + 1 = 0 and px + 8y - 7 = 0 are perpendicular to each other.

Miscellaneous Problems | Q 5 | Page 73

If the slope of one of the straight lines ax2 + 2hxy  by2 = 0 is thrice that of the other, then show that 3h2 = 4ab.

Miscellaneous Problems | Q 6 | Page 73

Find the values of a and b if the equation (a - 1)x2 + by2 + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.

Miscellaneous Problems | Q 7 | Page 73

Find whether the points (-1, -2), (1, 0) and (-3, -4) lie above, below or on the line 3x + 2y + 7 = 0

Miscellaneous Problems | Q 8 | Page 73

If (4, 1) is one extremity of a diameter of the circle x2 + y2 - 2x + 6y - 15 = 0 find the other extremity.

Miscellaneous Problems | Q 9 | Page 73

Find the equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).

Miscellaneous Problems | Q 10 | Page 73

Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)

## Chapter 3: Analytical Geometry

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Exercise 3.5Exercise 3.6Exercise 3.7Miscellaneous Problems

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 3 - Analytical Geometry

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