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

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Class 11th Business Mathematics and Statistics Answers Guide - Shaalaa.com
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Chapter 3: Analytical Geometry

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Exercise 3.5Exercise 3.6Exercise 3.7Miscellaneous Problems
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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 ₹ `1/5`x2 – 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]

Choose the correct answer

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
Class 11th Business Mathematics and Statistics Answers Guide - Shaalaa.com

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

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 3 (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 Business Mathematics and Statistics Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 3 Analytical Geometry are Locus, System of Straight Lines, Pair of Straight Lines, Circles, Conics.

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