#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 3: Analytical Geometry

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

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

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

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.

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

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.

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

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

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

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

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

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.

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

If the equation ax^{2} + 5xy – 6y^{2} + 12x + 5y + c = 0 represents a pair of perpendicular straight lines, find a and c.

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

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

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

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

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

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

**Find the centre and radius of the circle**

x^{2} + y^{2} = 16

**Find the centre and radius of the circle**

x^{2} + y^{2} – 22x – 4y + 25 = 0

**Find the centre and radius of the circle.**

5x^{2} + 5y^{2}+ 4x – 8y – 16 = 0

**Find the centre and radius of the circle.**

(x + 2) (x – 5) + (y – 2) (y – 1) = 0

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

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

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

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.

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.

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

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

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

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

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 x^{2} + y^{2} – 4x – 6y + 9 = 0.

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

Find the value of P if the line 3x + 4y – P = 0 is a tangent to the circle x^{2} + y^{2} = 16.

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

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

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

Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y^{2} – 8y – 8x + 24 = 0.

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

y^{2} = 20x

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

x^{2} = 8y

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

x^{2} = - 16y

The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ `1/5`x^{2} – 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.

The profit ₹ y accumulated in thousand in x months is given by y = -x^{2} + 10x – 15. Find the best time to end the project.

### 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

If m_{1} and m_{2} are the slopes of the pair of lines given by ax^{2} + 2hxy + by^{2} = 0, then the value of m_{1} + m_{2} is:

`(2"h")/"b"`

-`(2"h")/"b"`

`(2"h")/"a"`

-`(2"h")/"a"`

The angle between the pair of straight lines x^{2} – 7xy + 4y^{2} = 0 is:

`tan^-1 (1/3)`

`tan^-1 (1/2)`

`tan^-1 (sqrt33/5)`

`tan^-1 (5/sqrt33)`

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)

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

3

2

`1/3`

`1/2`

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

`7/5`

`-7/5`

`5/7`

`-5/7`

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`

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

If kx^{2} + 3xy – 2y^{2} = 0 represent a pair of lines which are perpendicular then k is equal to:

`1/2`

`-1/2`

2

- 2

(1, -2) is the centre of the circle x^{2} + y^{2} + ax + by – 4 = 0, then its radius:

3

2

4

1

The length of the tangent from (4, 5) to the circle x^{2} + y^{2} = 16 is:

4

5

16

25

The focus of the parabola x^{2} = 16y is:

(4 , 0)

(-4 , 0)

(0, 4)

(0, - 4)

Length of the latus rectum of the parabola y^{2} = -25x:

25

-5

5

-25

The centre of the circle x^{2} + y^{2} – 2x + 2y – 9 = 0 is:

(1, 1)

(-1, 1)

(-1, 1)

(1, -1)

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

x

^{2}– 2ax + y^{2}= 0y

^{2}– 2ay + x^{2}= 0x

^{2}+ y^{2}= a^{2}x

^{2}– 2ay + y^{2}= 0

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

x

^{2}+ y^{2}+ 2ax + 2by + 2b^{2}= 0x

^{2}+ y^{2}+ 2ax + 2by – 2b^{2}= 0x

^{2}+ y^{2}– 2ax – 2by – 2b^{2}= 0x

^{2}+ y^{2}– 2ax – 2by + 2b^{2}= 0

Combined equation of co-ordinate axes is:

x

^{2}– y^{2}= 0x

^{2}+ y^{2}= 0xy = c

xy = 0

ax^{2} + 4xy + 2y^{2} = 0 represents a pair of parallel lines then ‘a’ is:

2

-2

4

-4

In the equation of the circle x^{2} + y^{2} = 16 then v intercept is (are):

4

16

± 4

± 16

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}= 16x

^{2}+ y^{2}= 4

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}= 16x

^{2}+ y^{2}= 16

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

The eccentricity of the parabola is:

3

2

0

1

The double ordinate passing through the focus is:

focal chord

latus rectum

directrix

axis

The distance between directrix and focus of a parabola y^{2} = 4ax is:

a

2a

4a

3a

The equation of directrix of the parabola y^{2} = -x is:

4x + 1 = 0

4x - 1 = 0

x – 1 = 0

x + 4 = 0

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

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.

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

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.

If the slope of one of the straight lines ax^{2} + 2hxy by^{2} = 0 is thrice that of the other, then show that 3h^{2} = 4ab.

Find the values of a and b if the equation (a - 1)x^{2} + by^{2} + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.

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

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

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

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

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

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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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