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## Conic Sections Assignments Class 11 Mathematics

**Question. The length of transverse axis of the hyperbola 3x ^{2} – 4y^{2} = 32, is**

(a) 8√2/√3

(b) 16√2/√3

(c) 3/32

(d) 64/3

**Answer**

A

**Question. The equation of the hyperbola with vertices (3, 0), (–3, 0) and semi-latus rectum 4 is given by :**

(a) 4x^{2} – 3y^{2} + 36 = 0

(b) 4x^{2} – 3y^{2} + 12 = 0

(c) 4x^{2} – 3y^{2} – 36 = 0

(d) 4x^{2 }+ 3y^{2} – 25 = 0

**Answer**

C

**Question. The eccentricity of an ellipse, with its centre at the origin, is . 1/2 If one of the directrices is x = 4, then the equation of the ellipse is:**

(a) 4x^{2} + 3y^{2} = 1

(b) 3x^{2} + 4y^{2} = 12

(c) 4x^{2} + 3y^{2} = 12

(d) 3x^{2} + 4y^{2} = 1

**Answer**

B

**Question. The eccentricity of the curve 2x ^{2} + y^{2 }– 8x – 2y + 1= 0 is:**

(a) 1/2

(b) 1/√2

(c) 2/3

(d) 3/4

**Answer**

B

**Question. Radius of the circle (x + 5) ^{2} + (y – 3)^{2} = 36 is**

(a) 2

(b) 3

(c) 6

(d) 5

**Answer**

C

**Question. The value of p such that the vertex of y = x ^{2} + 2px +13 is4 units above the y-axis is**

(a) 2

(b) ± 4

(c) 5

(d) ± 3

**Answer**

D

**Question. The two conics y ^{2}/b^{2} + x^{2}/a^{2}= 1 and y^{2 }= − b/a x intersect if and only if**

(a) 0 < a ≤ 1/2

(b) 0 < b ≤ 1/2

(c) b

^{2 }> a

^{2}(d) b

^{2 }< a

^{2}

**Answer**

B

**Question. If the equation of ellipse is 9x ^{2} + 4y^{2} = 36, then **

Codes

A B C D

(a) 4 1 3 2

(b) 2 1 3 4

(c) 4 3 1 2

(d) 2 3 1 4

**Answer**

A

**Question. If a parabolic reflector is 20 cm in diameter and 5 cm deep, then the focus is**

(a) (2, 0)

(b) (3, 0)

(c) (4, 0)

(d) (5, 0)

**Answer**

D

**Question. The foci of an ellipse are (±2, 0) and its eccentricity is 1/2 then the equation of ellipse is x ^{2}/a^{2} + y^{2}/12= 1. The value of ‘a’ is**

(a) 3

(b) 4

(c) 6

(d) 2

**Answer**

B

**Question. The equation of a hyperbola with foci on the x-axis is**

**Answer**

A

**Question. The equation of a circle with centre at (1, 0) and circumference 10π units is**

(a) x^{2} + y^{2} – 2x + 24 = 0

(b) x^{2} + y^{2} – x – 25 = 0

(c) x^{2} + y^{2} – 2x – 24 = 0

(d) x^{2} + y^{2 }+ 2x + 24 = 0

**Answer**

C

**Question. A circle has radius 3 and its centre lies on the line y = x−1. The equation of the circle, if it passes through (7, 3), is**

(a) x^{2 }+ y^{2} + 8x − 6y +16 = 0

(b) x^{2} + y^{2} − 8x + 6y +16 = 0

(c) x^{2} + y^{2} − 8x − 6y −16 = 0

(d) x^{2} + y^{2} − 8x − 6y +16 = 0

**Answer**

D

**Question. The equation of the hyperbola whose foci are (– 2, 0) and (2, 0) and eccentricity is 2 is given by :**

(a) x^{2} – 3y^{2} = 3

(b) 3x^{2} – y^{2 }= 3

(c) – x^{2} + 3y^{2} = 3

(d) – 3x^{2 }+ y^{2} = 3

**Answer**

B

**Question. The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is**

(a) x^{2} + y^{2} = 9a^{2}

(b) x^{2} + y^{2} = 16a^{2}

(c) x^{2} + y^{2} = 4a^{2}

(d) x^{2} + y^{2} = a^{2 }

**Answer**

C

**Question. Tangents are drawn from the point (–2, –1) to the parabola y ^{2 }= 4x. If α is the angle between these tangent then the value of tan α is**

(a) 3

(b) 4

(c) –5

(d) 5

**Answer**

A

**Question. Which points on the curve x ^{2} = 2y are closest to the point (0, 5) ?**

(a) (± 2√2,4)

(b) (± 2,2)

(c) (± 3,9/2)

(d) (± 2,1)

**Answer**

A

**Question. Intercept on the line y = x by the circle x ^{2 }+ y^{2 }− 2x = 0 is AB. Equation of the circle on AB as a diameter is**

(a) x

^{2 }+ y

^{2 }+ x − y = 0

(b) x

^{2 }+ y

^{2 }− x + y = 0

(c) x

^{2 }+ y

^{2 }+ x + y = 0

(d) x

^{2 }+ y

^{2 }− x − y = 0

**Answer**

D

**Question. The equation 9x ^{2} – 16y^{2} – 18x + 32y – 151 = 0 represents a hyperbola**

(a) The length of the transverse axes is 4

(b) Length of latus rectum is 9

(c) Equation of directrix is x = 21/5 and x = –11/5

(d) None of these

**Answer**

C

**Question. The length of the line segment joining the vertex of the parabola y ^{2} = 4ax and a point on the parabola where the line segment makes an angle Θ to the x-axis is 4am/n. Here, m and n respectively are**

(a) sin Θ, cos Θ

(b) cos Θ, sin Θ

(c) cos Θ, sin

^{2}Θ

(d) sin

^{2}Θ, cos Θ

**Answer**

C

**Question. For the parabola y ^{2 }= –12x, equation of directrix is x = a. The value of ‘a’ is**

(a) 3

(b) 4

(c) 2

(d) 6

**Answer**

A

**Question. Equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity √3 is**

(a) 7x^{2} – 2y^{2} + 12xy – 2x + 9y – 22 = 0

(b) 5x^{2} – 2y^{2} + 10xy + 2x + 5y – 20 = 0

(c) 4x^{2} + 8y^{2} + 8xy + 2x – 2y + 10 = 0

(d) None of these

**Answer**

A

**Question. Length of the latus rectum of the hyperbola : x ^{2}/a^{2} − y^{2}/b^{2} = 1 is**

(a) b

^{2}/a

(b) 2b

^{2}/a

(c) a

^{2}/b

(d) 2a

^{2}/b

**Answer**

B

**Question. Equation of the circle concentric with the circle x ^{2 }+ y^{2 }– 3x + 4y – c = 0 and passing through the point (–1, – 2), is**

(a) x

^{2}+ y

^{2 }− 3x − 4y = 0

(b) x

^{2}+ y

^{2 }− 3x + 4y = 0

(c) x

^{2}+ y

^{2 }+ 3x + 4y = 0

(d) x

^{2}+ y

^{2 }– 7x + 7y = 0

**Answer**

B

**Question. The equation y ^{2 }+ 3 = 2(2x+ y) represents a parabola with the vertex at **

(a) (1/2,1)and axis parallel to y-axis

(b) (1,1/2) and axis parallel to x-axis

(c) (1/2,1) and focus at (3/2,1)

(d) (1,1/2) and focus at (3/2,1)

**Answer**

C

**Question. What is the radius of the circle passing through the points (0, 0), (a, 0) and (0, b) ?**

**Answer**

C

**Question. Equation of the circle which passes through the intersection of x ^{2} + y^{2 }+ 13x – 3y = 0 and 2x^{2} + 2y^{2}+ 4x – 7y – 25 = 0 whose centre lies on 13x + 30y = 0 is**

(a) x

^{2}+ y

^{2 }+ 5x + y = 0

(b) 4x

^{2}+ 4y

^{2}+ 30x −13y − 25 = 0

(c) 2x

^{2}+ 2y

^{2}+ 3x − 4y = 0

(d) 4x

^{2}+ 4y

^{2}− 8x + 7y +10 = 0

**Answer**

B

**Question. The eccentricities of the ellipse x ^{2}/α^{2} + y^{2}/β^{2 }= 1, α > β; and x^{2}/9 + y^{2}/16= 1 are equal. Which one of the following is correct ?**

(a) 4α = 3β

(b) αβ =12

(c) 4β = 3α

(d) 9α =16β

**Answer**

A

**Question. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2 . Then the length of the semimajor axis is**

(a) 8/3

(b) 2/3

(c) 4/3

(d) 5/3

**Answer**

A

**Question. The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is**

(a) x^{2} + y^{2 }– 2x – 2y + 1 = 0

(b) x^{2} + y^{2 }– 2x – 2y – 1 = 0

(c) x^{2} + y^{2 }– 2x – 2y = 0

(d) x^{2 }+ y^{2 }– 2x + 2y – 1 = 0

**Answer**

A

**Question. The equation of the ellipse whose axes are along the co-ordinate axes, vertices are (±5, 0) and foci at (±4, 0), is x ^{2}/25 + y^{2}/b^{2 }= 1. The value of b^{2} is**

(a) 3

(b) 5

(c) 9

(d) 4

**Answer**

C

**Question. The circle x ^{2} + y^{2 }– 8x + 4y + 4 = 0 touches :**

(a) x-axis only

(b) y-axis only

(c) both (a) and (b)

(d) None of these

**Answer**

B

**Question. The distance between the foci of a hyperbola is 16 and its eccentricity is √2. Its equation is**

(a) x^{2} – y^{2} = 32

(b) x^{2}/4 – y^{2}/9 = 1

(c) 2x – 3y^{2} = 7

(d) None of these

**Answer**

A

**Question. The eccentricity of the ellipse whose major axis is three times the minor axis is:**

(a) √2/3

(b) √3/2

(c) 2√2/3

(d) 2/√3

**Answer**

C

**Question. The equation of an ellipse with one vertex at the point (3, 1), the nearer focus at the point (1, 1) and e = 2/3 is : **

**Answer**

D

**Question. If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then radius of the circle is**

(a) 3/4

(b) 2/3

(c) 1/4

(d) 5/2

**Answer**

A

**Question. The locus of a point P(α, β) moving under the condition that the line y = αx +β is a tangent to the hyperbola x ^{2}/a^{2}− y^{2}/b^{2} = 1**

(a) an ellipse

(b) a circle

(c) a parabola

(d) a hyperbola

**Answer**

D

**Question. The equation of the circle with centre (0, 2) and radius 2 is x ^{2} + y^{2 }– my = 0. The value of m is**

(a) 1

(b) 2

(c) 4

(d) 3

**Answer**

C

**Question. Match the foci, centre, transverse axis, conjugate axis and vertices of hyperbola given in column-I with their corresponding meaning given in column-II**

Codes

A B C D E

(a) 4 3 1 5 2

(b) 1 4 3 5 2

(c) 4 1 5 3 2

(d) 4 1 3 5 2

**Answer**

D

**Question. The point diametrically opposite to the point P(1, 0) on the circle x ^{2} + y^{2 }+ 2x + 4y – 3 = 0 is**

(a) (3, – 4)

(b) (–3, 4)

(c) (–3, –4)

(d) (3, 4)

**Answer**

C

**Question. Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for**

(a) only one value of k

(b) 0 < k < 1

(c) k < 0

(d) all integral values of k

**Answer**

A

**Question. The vertex of the parabola x ^{2} + 8x + 12y + 4 = 0 is:**

(a) (– 4, 1)

(b) (4, –1)

(c) (– 4, –1)

(d) (4, 1)

**Answer**

A

**Question. The lines 2x − 3y = 5 and 3x − 4y = 7 are diameters of a circle having area as 154 sq.units.Then the equation of the circle is**

(a) x^{2} + y^{2 }− 2x + 2y = 62

(b) x^{2} + y^{2 }+ 2x − 2y = 62

(c) x^{2} + y^{2 }+ 2x − 2y = 47

(d) x^{2} + y^{2 }− 2x + 2y = 47 .

**Answer**

D

**Question. If (2, 0) is the vertex and the y-axis is the directrix of a parabola, then its focus is**

(a) (0, 0)

(b) (– 2, 0)

(c) (4, 0)

(d) (– 4, 0)

**Answer**

C

**Question. An ellipse has OB as semi minor axis, F and F ‘ its focii and the angle FBF ‘ is a right angle. Then the eccentricity of the ellipse is**

(a) 1/√2

(b) 1/2

(c) 1/4

(d) 1/√3

**Answer**

A

**STATEMENT TYPE QUESTIONS**

**Question. If equation of the ellipse is x ^{2}/100+ y^{2}/400 = 1, then**

**I. Vertices of the ellipse are (0, ± 20)**

**II. Foci of the ellipse are (0, ±10√3)**

**III. Length of major axis is 40.**

**IV. Eccentricity of the ellipse is √3/2.**

(a) I and II are true.

(b) III and IV are true.

(c) II, III, IV are true.

(d) All are true.

**Answer**

D

**Question. Consider the following statements.****I. Length of the latus rectum of the ellipse x ^{2}/a^{2} + y^{2}/b^{2 }= 1 is 2b^{2}/a**

**II. A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.**

(a) Only I is true.

(b) Only II is true.

(c) Both are true.

(d) Both are false.

**Answer**

C

**Question. I. The straight line passing through the focus and perpendicular to the directrix is called the axis of the conic section.****II. The points of intersection of the conic section and the axis are called vertices of the conic section.**

(a) Only I is true.

(b) Only II is true.

(c) Both are true.

(d) Both are false.

**Answer**

C

**Question. An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.****I. The two fixed points are called the foci of the ellipse. ****II. The mid point of the line segment joining the foci is called the centre of the ellipse.****III. The end points of the major axis are called the vertices of the ellipse.**

(a) Only I and II are correct.

(b) Only II and III are correct.

(c) Only I and III are correct.

(d) All are correct.

**Answer**

D

**Question. Consider the following statements.****I. A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.****II. A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not on the line) in the plane.**

(a) Only I is true

(b) Only II is true.

(c) Both are true.

(d) Both are false.

**Answer**

C

**Question. The centre of the circle 2r = 2 − 4r cosθ + 6 r sinθ is:**

(a) (2, 3)

(b) (– 2, 3)

(c) (– 2, – 3)

(d) (2, – 3)

## Answer

B

**Question. The point (2, 3) is a limiting point of a co-axial system of circles of which x ^{1} + y^{2} = 9 is a member. The coordinates of the other limiting point is given by:**

(a) (18/13 , 27/13)

(b) (9/13 , 6/13)

(c) (18/13 , –27/13)

(d) (–18/13 , –9/13)

## Answer

A

**Question. In the co-axial system of circle x ^{2} + y^{2} + 2gx + c = 0 where g is a parameter, if c > 0. Then the circles are:**

(a) Orthogonal

(b) Touching type

(c) Intersecting type

(d) Non intersecting type

## Answer

D

**Question. The equation of a circle of radius 1 touching the circles x ^{2} + y^{2} − 2|x|= 0 is: **

(a) x

^{2}+ y + 2 3x − 2= 0

(b) x

^{2}+ y − 2 3y + 2= 0

(c) x

^{2}+ y + 2 3y + 2= 0

(d) x + y + 2 3x + 2= 0

## Answer

B,C

**Question. The number of integral values of λ for which x ^{2} + y^{2} +λ x + (1−λ ) y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is:**

(a) 14

(b) 18

(c) 16

(d) 20

## Answer

C

**Question. If circles x ^{2} + y^{2} + 2ax + c = 0 and x^{2} + y^{2} + 2bx + c = 0 touch each other, then:**

(a) 1/a + 1/b = 1/c

(b) 1/a

^{2}+ 1/b

^{2}= 1/c

^{2}

(c) 1/a + 1/b = c

^{2}

(d) 1/a

^{2}+ 1/b

^{2}= 1/c

## Answer

D

**Question. If two circles (x−1) ^{2} + ( y−3)^{2} =r and x^{2} + y^{2} −8x+2y+8=0 intersect in two distinct points, then:**

(a) 2 < r < 8

(b) r = 0

(c) r < 2

(d) r > 2

## Answer

A

**Question. The equation of the circle whose radius is 5 and which touches the circle x ^{2} + y^{2} − 2x − 4y − 20 = 0 externally at the point (5, 5), is:**

(a) x

^{2}+ y

^{2}−18x −16y −120 = 0

(b) x

^{2}+ y

^{2}−18x −16y +120 = 0

(c) x

^{2}+ y

^{2}+18x +16y −120 = 0

(d) x

^{2}+ y

^{2}+18x −16y +120 = 0

## Answer

B

**Question. Centre of circle (x − x _{1})(x − x_{2}) +( y − y_{1})( y − y_{2}) = 0 is: **

## Answer

C

**Question. The centre of the circle, which cuts ortho-gonally each of the three circles x ^{2} + y^{2} +2x+17 y+4=0, x^{2} + y^{2} +7x+6y+11=0 and x^{2} + y^{2} − x + 22y + 3 = 0 is:**

(a) (3, 2)

(b) (1, 2)

(c) (2, 3)

(d) (0, 2)

## Answer

A

**Question. The equation of the circle through the points of intersection of the circles x ^{2} + y^{2} – 6x + 2y + 4 = 0, x^{2} + y^{2} + 2x – 4y – 6 = 0 and with its centre on the line y = x ?**

(a) 7x

^{2}+ 7y

^{2}+10x −10y −12 = 0

(b) 7x

^{2}+ 7y

^{2}−10x −10 y −12 = 0

(c) 7x

^{2}+ 7y

^{2}−10x +10y −12 = 0

(d) 7x

^{2}+ 7y

^{2}+10x +10 y +12 = 0

## Answer

B

**Question. The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is:**

(a) x^{2} + y^{2} − 2x − 2y +1 = 0

(b) x^{2} + y^{2} − 2x − 2y −1 = 0

(c) x^{2} + y^{2} − 2x − 2y = 0

(d) None of these

## Answer

A

**Question. The equation of the circle passing through the point (−1, − 3) and touching the line 4x + 3y −12 = 0 at the point (3, 0), is:**

(a) x^{2} + y^{2} − 2x + 3y − 3 = 0

(b) x^{2} + y^{2} + 2x − 3y − 5 = 0

(c) 2x^{2} + 2y^{2} − 2x + 5y −8 = 0

(d) None of these

## Answer

A

**Question. The of circle passing through (3,–6) and touching both the axes is **

(a) x^{2} + y^{2} − 6x + 6y + 9 = 0

(b) x^{2} + y^{2} + 6x − 6y + 9 = 0

(c) x^{2} + y^{2} + 30x − 30y + 225 = 0

(d) x^{2} + y^{2} − 30x + 30y + 225 = 0

## Answer

A,D

**Question. Equation of a circle with centre (4, 3) touching the circle x ^{2} + y^{2} =1 is **

(a) x

^{2}+ y

^{2}−8x − 6y − 9 = 0

(b) x

^{2}+ y

^{2}−8x − 6y +11 = 0

(c) x

^{2}+ y

^{2}−8x − 6y −11 = 0

(d) x

^{2}+ y

^{2}−8x − 6y + 9 = 0

## Answer

C,D

**Question. For the circle x ^{2} + y^{2} + 6x −8y + 9 = 0 , which of the following statements is true:**

(a) Circle passes through the point (−3, 4)

(b) Circle touches x-axis

(c) Circle touches y-axis

(d) None of these

## Answer

D

**Question. The locus of the centre of the circle which cuts a chord of length 2a from the positive x-axis and passes through a point on positive y-axis distant b from the origin is:**

(a) x^{2} + 2by = b^{2} + a^{2}

(b) x^{2} − 2by = b + a

(c) x^{2} + 2by = a −b

(d) x^{2} − 2by = b − a

## Answer

B

**Question. The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0 , is:**

(a) x^{2} + y^{2} + 4x −10y + 25 = 0

(b) x^{2} + y^{2} − 4x −10y + 25 = 0

(c) x^{2} + y^{2} − 4x −10y +16 = 0

(d) x^{2} + y^{2} −14y + 8 = 0

## Answer

B

**Question. A circle is concentric with the circle x + y − 6x +12y +15 = 0 and has area double of its are(a)**

The equation of the circle is:

(a) x^{2} + y^{2} − 6x +12y −15 = 0

(b) x^{2} + y^{2} − 6x +12y +15 = 0

(c) x^{2} + y^{2} − 6x +12y + 45 = 0

(d) None of these

## Answer

A

**Question. The range of values of a for which the point (a, 4) is outside the circles x ^{2} + y^{2} +10x = 0 and x^{2} + y^{2} −12x + 20 = 0 is:**

(a) (−∞,−8)∪(−2,6)∪(6,+∞)

(b) (– 8, – 2)

(c) (−∞,−8)∪(−2,+∞)

(d) None of these

## Answer

A

**Question. If the common chord of the circles x ^{2} + (y – λ)^{2} = 16 and x^{2} – y^{2} = 16 subtend a right angle at the origin, then λ is equal to:**

(a) 4

(b) 4√2

(c) ± 4√2

(d) 8

## Answer

C

**Question. The equation of the image of the circle x ^{2} + y^{2} + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0 is:**

(a) x

^{2}+ y

^{2}+ 32x − 4 y + 235 = 0

(b) x

^{2}+ y

^{2}+ 32x + 4y − 235 = 0

(c) x

^{2}+ y

^{2}+ 32x − 4 y − 235 = 0

(d) x

^{2}+ y

^{2}+ 32x + 4y + 235 = 0

## Answer

D

**Question. If the circles x ^{2} + y^{2} = a and x^{2} + y^{2} − 2gx + g − b = 0 touch each other externally, then:**

(a) g = ab

(b) g

^{2}= a

^{2}+ b

^{2}

(c) g

^{2}= ab

(d) g = a + b

## Answer

D

**Question. The abscissae of A and B are the roots of the equation x ^{2} + 2ax − b^{2} = 0 and their ordinates are the roots of the equation y^{2} + 2by − q^{2} = 0. The equation of the circle with AB as diameter is:**

(a) x

^{2}+ y

^{2}+ 2ax + 2by − b

^{2}− q

^{2}= 0

(b) x

^{2}+ y

^{2}+ 2ax + by − b

^{2}− q

^{2}= 0

(c) x

^{2}+ y

^{2}+ 2ax + 2by + b

^{2}+ q

^{2}= 0

(d) None of these

## Answer

A

**Question. If the straight line y = mx is outside the circle x ^{2} + y^{2} − 20 y + 90 = 0, then:**

(a) m > 3

(b) m < 3

(c) | m | > 3

(d) | m | < 3

## Answer

D