# MCQs for Mathematics Class 11 with Answers Chapter 11 Conic Sections

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Conic Sections with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

**Chapter 11 Conic Sections MCQ with Answers Class 11 Mathematics**

MCQ Questions Class 11 Mathematics Conic Sections with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. The equation Î»x ^{2} + 4xy + y^{2} + Î»x + 3y + 2 = 0 represents a parabola, if l is**

(a) -4

(b) 4

(c) 0

(d) None of these

## Answer

B

**Question. If the vertex of a parabola is the point (-3, 0) and the directrix is the line x + 5 = 0, then equation of parabola is**

(a) y^{2} = 8(x+ 3)

(b) x^{2} = 8(y+ 3)

(c) y2 = -8(x+ 3)

(d) y^{2} = 8(x+ 5)

## Answer

A

**Question. The focus of the parabola y ^{2} = 4y – 4x is**

(a) (0, 2)

(b) (1, 2)

(c) (2, 0)

(d) (2, 1)

## Answer

A

**Question. If the point P(4, -2) is one end of the focal chord PQ of the parabola y ^{2} = x , then the slope of the tangent at Q is**

(a) -1/4

(b) 1/4

(c) 4

(d) -4

## Answer

C

**Question. The length of latusrectum of the parabola 169{(x -1 ) + ( y – 3 ) ^{2} }=(5x – 12y + 17)^{2} is**

(a) 14/13

(b) 28/13

(c) 12/13

(d) None of these

## Answer

B

**Question. The equation of the parabola having vertex at the origin axis on the y-axis and passing through the point (6, – 3) is**

(a) y^{2} = 12 + 6

(b) x^{2} = 12y

(c) x^{2} = -12y

(d) y2 = -12x+ 6

## Answer

C

**Question. The equation of parabola having vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis is**

(a) 3x^{2} = 25y

(b) 2x^{2} = 25y

(c) 2y^{2} = 25x

(d) None of these

## Answer

B

**Question. If the normal to the parabola y ^{2} = 4ax at the pointP(at^{2} , at^{2}) cuts the parabola again at Q(aT^{2} , aT^{2} ) , then**

(a) -2â‰¤T â‰¤2

(b) T âˆˆ (-

**âˆž**, -8)âˆˆ(8,

**âˆž**)

(c) T

^{2}< 8

(d) T

^{2}â‰¥ 8

## Answer

D

**Question. If tangents at A and B on the parabola y ^{2} = 4ax intersect at point C,then ordinates of A, C and B are**

(a) always in AP

(b) always in GP

(c) always in HP

(d) None of these

## Answer

A

**Question. The locus of the middle points of the focal chords of parabola y ^{2}= 4ax is**

(a) y

^{2}= a(x-a)

(b) y

^{2}= 2a(x-a)

(c) y

^{2}= 4a(x-a)

(d) None of these

## Answer

B

**Question. The equation y ^{2} – 8y – x + 19 = 0 represents**

(a) a parabola whose focus is (1/4, 0) and directrix is x = -1/4

(b) a parabola whose vertex is (3, 4) and directrix is x = 1/4

(c) a parabola whose focus is (13/4, 4) and vertex is (0, 0)

(d) a curve which is not a parabola

## Answer

B

**Question. The sum of the distances of any point on the ellipse 3x ^{2} + 4y^{2} = 24 from its foci is **

(a) 4 âˆš2

(b) 8

(c) 16 âˆš2

(d) 2 âˆš2

**Answer**

A

**Question. The equation x2/1-r – y2/1+r = 1 ,Â |r| < 1Â represents a/an **

(a) ellipse

(b) hyperbola

(c) circle

(d) None of these

**Answer**

B

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

(a) x^{2} + y^{2} â€“ 2x + 24 = 0

(b) x^{2} + y^{2} â€“ x â€“ 25 = 0

(c) x^{2} + y^{2} â€“ 2x â€“ 24 = 0

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

**Answer**

C

**Question. If e1 is the eccentricity of the conic 9x ^{2} + 4y^{2} = 36 and e2 is the eccentricity of the conic 9×2 â€“ 4y^{2} = 36 then which is true ? **

(a) e

_{1}

^{2}+ e

_{2}

^{2}= 2

(b) 3 < e

_{1}

^{2}+ e

_{2}

^{ 2}< 4

(c) e

_{1}

^{2}+ e

_{2}

^{2}> 4

(d) None of these

**Answer**

B

**Question. The equation of the directrix of (x â€“ 1)2 = 2(y â€“ 2) is **

(a) 2y + 3 = 0

(b) 2x + 1 = 0

(c) 2x â€“ 1 = 0

(d) 2y â€“ 3 = 0

**Answer**

D

**Question. Find the equation of the parabola with focus (2, 0) and directrix x = â€“ 2. **

(a) x^{2} = 8y

(b) y^{2} = 4x

(c) x^{2} = 4y

(d) y2 = 8x

**Answer**

D

**Question. The eccentricity of the ellipse 12x ^{2} + 7y^{2} = 84 is equal to **

(a) âˆš5/7

(b) âˆš5/12

(c) âˆš5/12

(d) 5/7

**Answer**

B

**Question. Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2). **

(a) x^{2} = 8y

(b) x^{2} = 2y

(c) y^{2} = 4x

(d) y^{2} = 8x

**Answer**

A

**Question. The eccentricity of the hyperbola x2/a2Â –Â y2/b2 = 1Â which passes through the points (3, 0) and (3 âˆš2, 2) is **

(a) 1/âˆš13

(b) âˆš3

(c) âˆš13/2

(d) âˆš13/3

**Answer**

D

**Question. The distance between the vertex of the parabola y = x2 â€“ 4x + 3 and the centre of the circle x ^{2} = 9 â€“ (y â€“ 3)^{2} is **

(a) 2 âˆš3

(b) 3 âˆš2

(c) 2 âˆš2

(d) 2 âˆš5

**Answer**

D

**Question. The equation x2/14-a + y2/9-a = 1Â represents a/Â an **

(a) ellipse if a > 9

(b) hyperbola if 9 < a < 14

(c) hyperbola if a > 14

(d) ellipse if 9 < a < 14

**Answer**

B

**Question. The eccentricity of the hyperbola x ^{2} â€“ y^{2} = 2004 is **

(a) âˆš3

(b) 2

(c) 2 âˆš2

(d) âˆš2

**Answer**

D

**Question. If the equation of the parabola is x2 = â€“ 8y, the equation of the directix and length of latus rectum, respectively are **

(a) y = 3, 4

(b) y = â€“2, 4

(c) y = 2, 8

(d) y = â€“2, 8

**Answer**

C

**Question. The equation of hyperbola referred to its axes as axes of co-ordinate whose distance between the foci is 20 and eccentricity equals âˆš2 is **

(a) x^{2} â€“ y^{2} = 25

(b) x^{2} â€“ y^{2} = 50

(c) x^{2} â€“ y^{2} = 125

(d) x^{2} + y2 = 25

**Answer**

B

**Question. The two ends of latus rectum of a parabola are the points (3, 6) and (â€“ 5, 6). The focus is **

(a) (1, 6)

(b) (â€“ 1, 6)

(c) (1, â€“ 6)

(d) (â€“ 1, â€“ 6)

**Answer**

B

**Question. The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is **

(a) x = â€“ 1

(b) x = 1

(c) x = â€“ 3/2

(d) x = 3/2

**Answer**

D

**Question. If the ellipse x2/4 + y2/1Â = 1 meets theÂ ellipse x ^{2}/1 + y^{2}/a^{2}Â = 1 in four distinct points and a = b2 â€“ 10b + 25, then the value of b does not satisfy **

(a) (â€“ âˆž, 4)

(b) [4, 6]

(c) (6, âˆž)

(d) None of these

**Answer**

B

**Question. If the length of the major axis of an ellipse is 17/8 times the length of the minor axis, then the eccentricity of the ellipse is **

(a) 8/17

(b) 15/17

(c) 9/17

(d) 2âˆš2/17

**Answer**

B

**Question. Find the equation of the ellipse with foci at (Â± 5, 0) and x = 36/5Â as one of the directrices. **

(a) x^{2}/36 + y2/11 = 4

(b) x^{2}/6 + y2/11 =Â 1

(c) x^{2}/36 + y2/11 = 1

(d)Â x2/36 + y2/4Â = 1

**Answer**

C

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

(a) 4x^{2} â€“ 3y^{2} + 36 = 0

(b) 4x^{2} â€“ 3y^{2} + 12 = 0

(c) 4x^{2} â€“ 3y^{2} â€“ 36 = 0

(d) None of these

**Answer**

C

**Question. The parametric coordinates of any point on theÂ parabola y ax 2 = 4 can be**

(a) (a – at^{2},- 2at)Â

(b) (a – at^{2}, 2at)Â

(c) (a sin^{2}t, a sint^{-2})Â Â

(d) (a sint, -2a cos t)

## Answer

C

**Question. The tangent to the parabola y ^{2 }= 4ax at the point (a, 2a)makes with x-axis an angle equal to**

(a) Ï€/3

(b) Ï€/4

(c) Ï€/2

(d) Ï€/6

## Answer

B

**Question. The normals at three points P, Q, Rof the parabola y ^{2} = 4ax meet in (h, k). The centroid of DPQRlies on**

(a) x = 0

(b) y = 0

(c) x = – a

(d) y = a

## Answer

B

**Question. At what point on the parabola y ^{2} = 4x , the normal makes equal angles with the coordinate axes?**

(a) (4, 4)

(b) (9, 6)

(c) (4, -4)

(d) (1, -2)

## Answer

D

**Question. The circle x ^{2} + y^{2} = 5 meets the parabola y^{2} = 4x at P and Q. Then,the length PQ is equal to**

(a) 2

(b) 2âˆš2

(c) 4

(d) None of these

## Answer

C

**Question. Equation ax ^{2} + 2hxy + by^{2} + 2 gx + 2fy + c = 0**

**(abc + 2fgh – af**

^{2}– bg^{2}– ch2 â‰ 0) represents a parabola, if(a) h

^{2}= ab

(b) h

^{2}> ab

(c) h

^{2}< ab

(d) None of these

## Answer

A

**Question. The equation (x-2) ^{2} + ( y-3)^{2} = (3x+4y-2/5)^{2} represents**

(a) a parabola

(b) a pair of straight lines

(c) an ellipse

(d) a hyperbola

## Answer

A

**Question. The equation of latusrectumof a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12 , then length of the latusrectum is**

(a) 4âˆš2

(b) 2âˆš2

(c) 8

(d) 8âˆš2

## Answer

D

**Question. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y ^{2} = 4ax is another parabola with the directrix**

(a) x = – a

(b) x= – 2

(c) x = 0

(d) x = a/2

## Answer

C

**Question. The coordinates of a point on the parabola y ^{2} = 8x whose focal distance is 4, is **

(a) (â€“ 2, â€“ 4), (2, â€“ 4)

(b) (2, 4), (2, â€“ 4)

(c) (1, 4), (2, â€“ 4)

(d) (2, â€“ 4), (â€“ 2, 4)

## Answer

B

**Question. If the parabola y ^{2} = 4ax passes through the point (3, 2), then the length of its latusrectum is**

(a) 2/3

(b) 4/3

(c) 1/3

(d) 4

## Answer

B

**Question. The parabola y ^{2} = 8x and the circle x^{2} + y^{2} = 2**

(a) have only two common tangents which are mutually perpendicular

(b) have only two common tangents which are parallel to each other

(c) have infinitely many common tangents

(d) does not have any common tangent

## Answer

A

**Question. If (9a,6a) is a point bounded in region formed by parabola y ^{2} = 16x and x = 9, then**

(a) a âˆˆ (0,1)

(b) a < 1/4

(c) a < 1

(d) 0 < a < 4

## Answer

A

**Question. The length of the latusrectum of the parabola****169 {(x – 1) + ( y – 3) ^{2}} = (5x -12y + 17)^{2} is**

(a) 14/13

(b) 12/13

**(c) 28/13**

(d) None of these

## Answer

C

**Question. x – 2 = t ^{2}, y = 2t are the parametric equations of the parabola**

(a) y

^{2}= 4x

(b) y

^{2}= -4x

(c) x

^{2}= -4y

(d) y

^{2}= 4( – 2)

## Answer

D

**Question. The latusrectum of the parabola y ^{2} = 5x + 4y + 1is**

(a) 5/4

(b) 10

(c) 5

(d) 5/2

## Answer

A

**Question. The parametric equation of a parabola is x = t ^{2} + 1,y = 2 t + 1. The cartesian equation of its directrix is**

(a) x = 0

(b) x + 1 = 0

(c) y = 0

(d) None of the above

## Answer

A

**Question. The latusrectum of the parabola y ^{2} = 4ax whose focal chord is PSQ such that SP = 3 and SQ = 2 , is given by**

(a) 24/5

(b) 12/5

(c) 6/5

(d) 1/5

## Answer

A

**Question. If a focal chord of the parabola y ^{2} = ax is 2x – y – 8 = 0, then the equation of the directrix is**

(a) x + 4 = 0

(b) x – 4 = 0

(c) y – 4 = 0

(d) y + 4 = 0

## Answer

A

**Question. The position of the point (â€“ 2, 2) with respect to the parabola y ^{2} – 4y + 9x + 13 = 0 is**

(a) inside

(b) outside

(c) on

(d) None of these

## Answer

A

**Question. If the point (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then the equation of the parabola is**

(a) x^{2} + 8y = 16

(b) x^{2} + 8y = 32

(c) x^{2 }+ 16y = 30

(d) x^{2} – 8y = 32

## Answer

B

**Question. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0, is**

(a) x^{2} + y^{2} -2xy – 4x + 4y – 4 = 0

(b) x^{2} + y^{2} – 2xy + 4x – 4y – 4 = 0

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

(d) x^{2} + y^{2} – 2xy – 4x – 4y + 4 = 0

## Answer

C

**Question. Angle between the tangents drawn to y ^{2} = 4x at the points where it is intersected by the line y = x – 1 is equal to**

(a) Ï€/4

(b) Ï€/3

(c) Ï€/6

(d) Ï€/2

## Answer

D

**Question. The equation of parabola having vertex (0, 0) passing through (2, 3) and axis is along x-axis is**

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

(b) y^{2} = 9/2x

(c) y^{2} = -9/2x

(d) x^{2 }= -9/2x

## Answer

B

**Question. The angle made by a double ordinate of length 8a at the vertex of the parabola y ^{2} = 4ax is**

(a) Ï€/3

(b) Ï€/2

(c) Ï€/4

(d) Ï€/6

## Answer

B

**Question. The equation of tangent to the parabola y2= 9x which goes through the point (4, 10), is**

(a) x + 4y + 1= 0

(b) 9x + 4y + 4 = 0

(c) x – 4y + 36 = 0

(d) 9x + 4y + 9 = 0

## Answer

C

**Question. If the tangent at the point P(2, 4) to the parabola y x 2 = 8 meets the parabola y ^{2} = 8x + 5 at Q andR, then the mid-point of the QRis**

(a) (2, 4)

(b) (4,2)

(c) (7, 9)

(d) None of these

## Answer

B

**Question. The angle of intersection between the curves x ^{2} = 4(y+1) and x^{2} = -4(y+1) is**

(a) Ï€/6

(b) Ï€/4

(c) 0

(d) Ï€/2

## Answer

A

**Question. If the line x cos a + y sin a = p touches the parabola y ^{2} = 4ax , then point of contact is**

(a) (a tan

^{2}Î± , 2a tanÎ±)

(b) (a tan2Î±, 2a tanÎ±)

(c) (a tanÎ±, 2a tanÎ±)

(d) None of these

## Answer

A

**Question. Two perpendicular tangents to y ^{2} = 4ax always intersect on the line, if**

(a) x = a

(b) x + a = 0

(c) x + 2a = 0

(d) x + 4a = 0

## Answer

B

**Question. The equation of the tangent to the parabola y ^{2} = 9 which goes through the point (4, 10), is**

(a) x + 4 y + 1 = 0

(b) 9x + 4 y + 4 = 0

(c) x + 4 y + 36 = 0

**(d) 9x – 4 y + 4 = 0**

**Question. The tangents drawn from the ends of latusrectum of y ^{2} = 12 meets at**

(a) directrix

(b) vertex

(c) focus

(d) None of these

## Answer

A

**Question. The shortest distance between the parabola y2 = 4x and the circle x ^{2} + y^{2 }+ 6x – 12y + 20 = 0 is**

(a) 4âˆš2 – 5

(b) 0

(c) 3âˆš2 + 5

(d) 1

## Answer

A

**Question. The ends of a line segment are P(1, 3) and Q(1, 1). R is a point on the line segment PQ such that PR:QR = 1:l. If Ris an interior point of the parabola y ^{2 }= 4x , then**

(a) Î» âˆˆ(0,1)

(b) Î» âˆˆ (-3/5,1)

(c) Î» âˆˆ (1/2 ,3/5)

(d) None of these

## Answer

A

**Question. If tangents at A and B on the parabola y ^{2} = 4 intersect at pointC, then ordinates of A,C and Bare**

(a) always in AP

(b) always in GP

(c) always in HP

(d) None of these

## Answer

A

**Question. The number of real tangents that can be drawn to the curve y ^{2} + 2xy + x^{2} + 3y + 1 = 0 from the point (1, – 2) is**

(a) one

(b) two

(c) zero

(d) None of these

## Answer

C

**Question. Number of common tangents to the parabola y ^{2} = 4ax and x^{2} = 4by is**

(a) 4

(b) 3

(c) 2

(d) 1

## Answer

D

**Question. If the tangent to the parabola y ^{2} = ax makes an angle of 45Â° with x-axis, then the point of contact is**

(a) (a/2 , a/2)

(b) (a/4 , a/4)

(c) (a/2 , a/4)

(d) (a/4 , a/2)

## Answer

D

**Question. Tangent at the vertex divides the distance between directrix and latusrectum in the ratio**

(a) 1 : 1

(b) 1 : 2

(c) depends on directrix and focus

(d) None of the above

## Answer

A

We hope the above MCQ Questions Class 11 Mathematics Conic Sections with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Conic Sections is an important chapter in Class 11 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefits of class 11 students. Please go through these and let us know if you have any feedback in the comments section.