MCQs For NCERT for Class 11 Mathematics Chapter 11 Conic Sections

Please refer to the MCQ Questions for Class 11 Conic Sections Maths Chapter 11 with Answers. The following Conic Sections Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Conic Sections with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

Conic Sections Class 11 MCQ Questions with Answers

See below Conic Sections Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. Find an equation of the circle with centre at   
(0, 0) and radius r.
(a) x² + y² = r²
(b) x² – y² = r²
(c) x – y = r
(d) x² + r² = y²

Question: The area of the circle centred at (1, 2) and passing through (4, 6) is
(a) 5π
(b) 10π
(c) 25π
(d) None of these 

Question: If the area of the circle 4x²+4y²-8x+16y+k=0   is 9π sq units, then the value of k is
(a) 4
(b) 16
(c) − 16
(d) ± 16 

Question: The distinct points A (0,0 ) B( 0,1)C (1,0 ) and D (2a, 3a)are concyclic, then
(a) ‘a’ can attain only rational values
(b) a is irrational
(c) cannot be con cyclic for any a
(d) None of the above

Question: If a circle passes through the point (0, 0), (a ,0 )  and ( 0, b)  then find the coordinates of its centre.
(a) (− a/2,-b/2)
(b) (a/2, b/2)
(c) (−a/1,b/2)
(d) None of these

Question: The area of square inscribed in a circle x²+y²-6x-8y=0 is
(a) 100 sq units
(b) 50 sq units
(c) 25 sq units
(d) None of these

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) x²+ y²  = 9a²
(b) x²+ y² = 16a²
(c) x²+ y² = 4a²
(d) x²+ y² = a²

Question: If the tangent at the point P on the circle x²+y²+6x+6y=2 meets the straight line 5x-2y+6=0 = at a point Q on the y-axis, then the length of PQ is
(a) 4
(b) 2 5
(c) 5
(d) 3 5

Question: The range of α, for which the point (  α, α ) α α lies inside the region bounded by the curves y = √1-x² and x +y = 1 is
(a) 1/2<α< 1/√2
 (b)1/2<α< 1/3
(c) 1/3<α 1/√3 
(d) 1/4<α< 1/2 

Question: Let PQ PS and be tangents at the extremities of the diameter PR of a circle of radius r. If PS RQ and intersect at a point x on the circumference of the circle, then 2r equals
(a) √PQ ⋅ RS
(b) PQ+ RS /2
(c) 2PQ⋅ RS/PQ+ RS
(d) √PQ²+ RS²/2 

Question. In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is   
(a) 3/5
(b) 1/2
(c) 4/5
(d) 1/√5

Question. Eccentricity of ellipse x² /a² + y²/b² = 1 if it passes through point (9, 5) and (12, 4) is   
(a) √3/ 4
(b) √4 / 5
(c) √5 / 6
(d) √6/ 7

Question: If the circles x 2+Y2+2X+2KY+6=0 and X2+Y2+2KY+K=0  0intersect orthogonally, then k is
(a) 2 or −3/2
(b) − 2 or 3/2
(c) 2 or 3/2
(d) − 2 or 3/2 

Question: If the circle S1:x²+y²=16 intersects another circle S1 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4 , the coordinates of the centre of S₂ are
(a) (−9/5,12/5),(9/5,12/5)
(b) (−9/5,-12/5),(9/5,12/5),
(c) (12/5,9/5),(12/5,9/5)
(d) None of these 

Question: The circles x²+Y²+ 2g₁x-a²=0 and x²+y²+2g₂x-a²=0 cut each other orthogonally.
If p₁ and p₂ are perpendiculars from( 0, a) and (0,a ) on a common tangent of these circles, then p₁ p₂ is equal to
(a) a²/2
(b) a²
(c) 2a²
(d) a²+2

Question: The locus of the centre of circle which cuts the circles x²+Y²+4X-6Y+9=0  and x²+Y²-4X+6Y+4=  0 orthogonally, is
(a) 12X+8Y+5=0 
(b) 8X+12Y+5=0 
(c) 8X-12Y+5=0 
(d) None of these 

Question: The lengths of the tangents from any point on the circle 15x²+15y²-48x+64y=0  to the two circles 5x²+5y²-24x+32y+75=0, 5x²+5y²-48x+64y+300=0, are in the ratio
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) None of these 

Question: If the area of the circle 4x²+4y²-8x+16y+k=0  is 9π sq units, then the value of k is
(a) 4
(b) 16
(c) − 16
(d) ± 16 

Question: If the radical axis of the circles

(a) g =3/4 and f≠ 2
(b) g ≠ 3/4 and f=2
(c) g = 3/4 or f=2
(d) None of these 

Question: The locus of the mid-point of the chord of the circle x²+y²-2x-2y-2=0,  which makes an angle of 120° at the centre, is
(a) x²+y²-2x-2y+1=0 
(b) x²+y²+x+y-1=0 
(c) x²+y²-2x-2y-1=0 
(d) None of the above 

Question: P (a,b) be any point such that the length of tangents from P to both the circles x²+y²-6x-8y=0  and x²+y²-12x-16y+12=0 are equal, then
(a) 3a+4b-6=0
(b)3a-4b+6=0
(c) 6a-8b+12=0
(d) 4a-3b+7=0 

Question. The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is 
(a) (x – 2) + (y – 2) = 13
(b) (x – 2)² + (y – 2)² = 13
(c) (x)² + (y)² = 13
(d) (x – 4)² + (y – 5)² = 13

Question. The equation of the directrix of the parabola   
y² + 4y + 4x + 2 = 0 is :
(a) x = –1
(b) x = 1
(c) x =-3/2
(d) x = 3/2 

Question. The foci of the ellipse 25 (x + 1)² + 9(y + 2)² = 225 are at :   
(a) (–1, 2) and (–1, –6)
(b) (–2, 1) and (–2, 6)
(c) (–1, –2) and (–2, –1)
(d) (–1, –2) and (–1, –6)

Question. The eccentricity of the hyperbola   
x² – 3y² = 2x + 8 is
(a) 2/3
(b) 1/3
(c) 2/√3
(d) 3/2

Question. If the parabola y² = 4 ax passes through the point (3, 2), then the length of its latusrectum is

Question. If the focal distance of a point on the parabola y² = 12x is 4 units, then the abscissa of that point is
(a) 5
(b) 1
(c) 2
(d) − 1

Question. In an ellipse, if ends of major axis are (0,± √5) and ends of minor axis are (±1,0), then the equation of ellipse is given by

Question. In an ellipse, if length of major axis is 26 units and foci are (± 5,0), then the equation of ellipse is given by

Question. If the foci and vertices of an ellipse be (±1, 0) and (±2, 0) respectively, then the minor axis of the ellipse is
(a) 2 √5 units
(b) 2 units
(c) 4 units
(d) 2 √3 units

Question What is the difference of the focal distances of any point on the hyperbola?   
(a) Eccentricity
(b) Distance between foci
(c) Length of transverse axis
(d) Length of semi-transverse axis

Question. The one which does not represent a hyperbola is :   
(a) xy = 1
(b) x² – y² = 5
(c) (x – 1) (y – 3) = 0
(d) x² – y² = 0

Question. For what value of k, does the equation 9x² + y² = k (x² – y² – 2x) represent equation of a circle ?   
(a) 1
(b) 2
(c) –1
(d) 4

Question. The equation xy = 1 represents:   
(a) straight line
(b) pair of straight line
(c) an ellipse
(d) a hyperbola 

Question. What is the radius of the circle passing through the points (0, 0), (a, 0) and (0, b) ?     
(a) √(a² – b²)(b) √(a² + b²)
(c) 1/2√a² – b²
(d) 2√(a² + b²)

Question. What is the length of the smallest focal chord of the parabola y² = 4ax ?   
(a) a
(b) 2a
(c) 4a
(d) 8a

Question. The equation of the hyperbola with vertices (3, 0), (–3, 0) and semi-latus rectum 4 is given by :   
(a) 4x² – 3y² + 36 = 0
(b) 4x² – 3y² + 12 = 0
(c) 4x² – 3y² – 36 = 0
(d) 4x² + 3y² – 25 = 0

Question. A conic section with eccentricity e is a parabola if:   
(a) e = 0
(b) e < 1
(c) e > 1
(d) e = 1

Question. The distance between the foci of a hyperbola is 16 and its eccentricity is 2. Its equation is   
(a) x² – y² = 32  
(b) x²/4 – Y²/9 = 1
(c) 2x – 3y² = 7
(d) none of these

.Question. If the equation of a circle is  (4a – 3)x² + ay² + 6x – 2y + 2 = 0 , then its centre is
(a) (3, -1)
(b) (3, 1)
(c) (–3, 1)
(d) None of these

Question. The equation of the parabola with vertex at origin, which passes through the point (–3, 7) and axis along the x-axis is   
(a) y² = 49x
(b) 3y² = – 49x
(c) 3y² = 49x
(d) x² = – 49y

Question. The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be   
(a) 2/3
(b) √2/3
(c) 1/√3
(d) 1/√2

Question. Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity √2/5 is   
(a) 5x² + 3y² – 48 = 0
(b) 3x² + 5y² – 15 = 0
(c) 5x² + 3y² – 32 = 0
(d) 3x² + 5y² – 32 = 0

Question. The equation of the hyperbola whose foci are (– 2, 0) and (2, 0) and eccentricity is 2 is given by :   
(a) x² – 3y² = 3
(b) 3x² – y² = 3
(c) – x² + 3y² = 3
(d) – 3x² + y² = 3

Question. The value of p such that the vertex of y = x² + 2px +13 is 4 units above the y-axis is 
(a) 2
(b) ± 4
(c) 5
(d) ± 3

Question. Point (1, 2) relative to the circle x² + y² + 4x – 2y – 4 = 0 is a/an   
(a) exterior point
(b) interior point, but not centre
(c) boundary point
(d) centre

Question. For the ellipse 3x² + 4y² = 12 length of the latus rectum is:   
(a) 3
(b) 4
(c) 3/5
(d) 2/5

Question: If the abscissae and ordinates of two points P and Q are roots of the equations x² +2ax -b²=0 and y²+ 2p-y q² =0 respectively, then the equation of the circle with PQ as diameter, is
(a) x²+ y²+ 2ax +2py- b²– q² =0
(b) x²+ y²– 2ax- 2py+ b² +q²=0
(c) x²+ y²– 2ax- 2py- b² -q²=0
(d) x²+ y²⁺2ax+2py+ b² +q²=0 

Question: If (mi,1/mi),i=1,2,3,4  are con cyclic points, then the value of m₁ m m₂ m₃  m₄ is
(a) 1
(b) − 1
(c) 0
(d) None of these

Question: If (a cos θ_i , a sin θ_i), i = 1, 2, 3   represent the vertices of an equilateral triangle inscribed in a circle, then 
(a) cosθ₁ + cosθ₂ + cosθ₃ =0
(b) secθ₁ +secθ₂ + secθ₃ =0
(c) tanθ₁ + tanθ₂ + tanθ₃ =0 
(d) cotθ₁ + cotθ₂ + cot θ₃ =0   

Question: If the area of the quadrilateral formed by the tangent from the origin to the circle x²+y²+6x-10y+c=0  and the pair of radii at the points of contact of these tangents to the circle is 8 sq units, then c is a root of the equation
(a) c^{2 –}32c +64 =0
(b) c² -34c +64 =0 
(c) c² +2c  -64 =0 
(d) c² +34 -64 =0 

Question. In a parabola semi-latusrectum is the harmonic mean of the:   
(a) segment of a chord
(b) segment of focal chord
(c) segment of the directrix
(d) none of these

Question. The focal distance of a point on the parabola y² = 12x is 4. What is the abscissa of the point ?   
(a) 1
(b) – 1
(c) 2√3
(d) – 2

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) 4x² + 3y² = 1
(b) 3x² + 4y² = 12
(c) 4x² + 3y² = 12
(d) 3x² + 4y² = 1

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 semi-major axis is   
(a) 8/3
(b) 2/3
(c) 4/3
(d) 5/3

Question. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at   
(a) (0, 2)
(b) (1, 0)
(c) (0, 1)
(d) (2, 0)

Question. The length of the latus rectum of the ellipse 9×2 + 16y2 = 144 is
(a) 4
(b) 11/4
(c) 7/2
(d) 9/2

Question. The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is
(a) 12x² – y² + 4xy – 78y = 0
(b) 14x² + y² + 8xy – 4x + 2y – 4 = 0
(c) 12x² + y² + 4xy – 78x = 0
(d) 16x² + y² + 8xy – 74x – 78y + 212 = 0

Question. The equation of the ellipse whose focus is (1, – 1), directrix is the line x – y – 3 = 0 and the eccentricity is 1/√2, is
(a) 3x² + 2xy + 3y² – 2x + 2y – 1 = 0
(b) 3x² + 2xy + 3y² + 2 = 0
(c) 3x² + 2xy + 3y² + 2x – 2y – 1 = 0
(d) None of these

Question. If the vertex of the parabola y = x2 – 16x + K lies on x-axis, then the value of K is
(a) 16
(b) 8
(c) 64
(d) – 64

Question. The equation of family of circles with centre at (h, k) touching the x-axis is given by
(a) x² + y² – 2hx + h2 = 0
(b) x² + y² – 2hx – 2ky + h2 = 0
(c) x² + y² – 2hx – 2ky – h2 = 0
(d) x² + y² – 2hx – 2ky = 0

Question. If for the ellipse x2/a2 + y2/b2 = 1 , y-axis is the minor axis and the length of the latus rectum is one half of the length of its minor axis, then its eccentricity is
(a) 1/√2
(b) 1/2
(c) √3/2
(d) 3/4

Question. Find the equation of the circle with centre (–3, 2) and radius 4.
(a) (x + 3)² + (y – 2)² = 16
(b) (x – 3)² + (y – 2)² = 9
(c) (x + 3)² + (y + 2)² = 25
(d) x2 + y2 = 25

Question. Find the centre and the radius of the circle x² + y² + 8x + 10y – 8 = 0.
(a) (5, 4), – 7
(b) (–4, –5), 7
(c) (4, –5), 7
(d) (5, –4), 7

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) x² + y² – 2x – 2y + 1 = 0
(b) x² + y² – 2x – 2y – 1 = 0
(c) x² + y² – 2x – 2y = 0
(d) x² + y² – 2x + 2y – 1 = 0

Question. If the circle x² + y² – 17x + 2fy + c = 0 passes through (3, 1), (14, –1) and (11, 5), then c is
(a) 0
(b) –41
(c) –17/2
(d) 41

Question. The eccentricity of an ellipse x2/a2 + y2/b2 = 1 whose length of latus rectum is half of the length of its major axis is
(a) 1/√2
(b) √2/3
(c) √3/2
(d) None of these 

Question. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–6, 1) and (4, –4) is
(a) 3x² – 4y² = 32
(b) 3x² + 4y² = 112
(c) 4x² – 3y² = 112
(d) 4x² + 3y2 = 112

Question. Find the coordinates of the foci and eccentricity respectively of the ellipse x2/25 + y2/9 = 1 .
(a) (0, ± 4), 4/5
(b) (±4, 0), 4/5
(c) (0,± 4),4/3
(d) (0, ± 2), 4/5

Question. Find the coordinates of the foci and the length of the latus rectum of the hyperbola x2/9 – y2/16 = 1.
(a) (0, ±2), 32/3
(b) (0, ±5),32/3
(c) (±5 , 0),32/3
(d) (0, ±5),3/32

Question. The sum of the distances of a point (2, – 3) from the foci of an ellipse 16(x – 2)2 + 25 (y + 3)2 = 400 is
(a) 8
(b) 6
(c) 50
(d) 32

Question. The eccentricity of the conic (x+2)2 + (y – 1)2 = 1 is
(a) √7/8
(b) √6/17
(c) √6/7
(d) √6/11

Question. If the foci of the ellipse x2/9 + y2/16 = 1 are (0, √7) and (0, − √7) , then the foci of the ellipse x2/9+t² + y2/6+t² = , t ∈ R, are
(a) (0, √7), (0, − √7)
(b) (0, √7), (0, – √7)
(c) (0, 2 √7), (0, − 2 √7)
(d) ( √7, 0), (− √7, 0)

Question. Find the equation of the parabola which is symmetric about the y-axis, and passes through the point (2, –3).
(a) x2 = 4y
(b) 4y = 3x²
(c) 3x² = – 4y
(d) 3y = – 4x²

Question. The eccentricity of the hyperbola − x²/a² + y²/b² = 1 is given by
(a) e = √a²+b²/a²
(b) e = √a²-b²/a²
(c) e = √b²-a²/a²
(d) e = √a²+b²/b²

Question. If (4, 0) is a point on the circle x2 + ax + y2 = 0, then the centre of the circle is at
(a) (–2, 0) 
(b) (0, 2)
(c) (2, 0)
(d) (1, 0)

Question. The equation of the circle with centre (− 3,2) and radius 4 units, is
(a) (x − 3)² + (y − 2)² = 16 
(b) (x + 3)² + (y + 2)² = 16 
(c) (x − 3)² + (y + 2)² = 16 
(d) (x + 3)² + (y − 2)² = 16

Question. If the equation of circle is x² y² 2x + − 2 + 4y − 8 = 0, then its centre (C) and radius (r) respectively are
(a) (–2, 4) and √13 units
(b) (–1, 2) and √13 units
(c) (1, –2) and √13 units
(d) (2, –4) and √13 units

Question. The equation of the circle having centre at (− 3, 5) and touching the line 7x − 8y + 8 = 0 is

Question. If the equation of parabola is y² = 12x , then
(a) focus = (3, 0)
(b) length of latusrectum is 12 units
(c) directrix is x = − 3 and axis of symmetry is X-axis
(d) All of the above

Question. If parabola is passing through (2, 3), vertex (0, 0) and axis is along X-axis, then the equation of parabola is

Question. If parabola is passing through (5, 2), vertex (0, 0) and symmetric with respect to Y-axis, then the equation of parabola is

Question. If the focus of a parabola is (0, − 3) and its directrix is y = 3, then its equation is
(a) x² = − 12y
(b) x² = 12y
(c) y² = − 12x
(d) y² = 12x

Question. The length of the latusrectum of an ellipse is 1/3 unit of the major axis. Its eccentricity is

Question. The length of the latusrectum of the ellipse 3×2 + y2 = 12 is
(a) 4 units
(b) 3 units
(c) 8 units
(d) (4/√2) units

Question. The equation of ellipse whose eccentricity is 2/3, latusrectum is 5 units and the centre is (0, 0) is given by

Question. If the equation of ellipse is

then which of the following is not correct?
(a) Foci = (± √13, 0) and vertices = (± 7, 0)
(b) Length of major axis is 14 units and length of minor axis is 12 units

(d) Length of latusrectum is 72/7 units

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

Question. If the vertices of hyperbola are (±7, 0) and its eccentricity is 4/3, then the equation of hyperbola is

Question. The equation of the hyperbola with vertices at (0,± 6) and eccentricity 5/3 is

Question. The equation of the hyperbola with eccentricity 3/2 and foci at (± 2, 0) is

Case Based MCQs

A man running on a race course notices that sum of its distances from two flag posts from him is always 10m and the distance between the flag posts is 8 m.
He notes that he can read the messages of value system ‘Honesty’ and ‘Respect for other’ on the poles which ever side he moves, then answer the following questions which are based on above it.

Question. The path traced by the man will be
(a) an ellipse
(b) a parabola
(c) a hyperbola
(d) a circle

Question. Value of a for the standard equation of path is
(a) 10
(b) 5
(c) 15
(d) 20

Question. Value of b for the standard equation of path is
(a) 3
(b) 4
(c) 5
(d) 6

Question. Equation of path is

Question. Value of (2 a + b) is
(a) 10
(b) 13
(c) 15
(d) 18

Due to heavy storm, an electric wire got bent as shown in figure. It followed a mathematical shape. Answer the following question below.

Question. Name the shape in which the wire is bent
(a) circle
(b) parabola
(c) ellipse
(d) hyperbola

Question. The equation of the shape of curve is

Question. The eccentricity of the given shape is
(a) 2/3
(b) √x/√3
(c) √5/3
(d) √5/4

Question. The length of the latusrectum of the shape is
(a) 9 units
(b) 8/3 units
(c) 4/3 units
(d) None of the above

Question. Foci of the shape is
(a) (± 3, 0)
(b) (± √5, 0)
(c) (0, ± 2)
(d) (0, ± √5)

Assertion & Reasoning Based Questions :

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : Eccentricity is always less than 1.
Reason : Foci are at a distance of ae from the centre.

Question. Assertion : A line through the focus and perpendicular to the directrix is called the x-axis of the parabola.
Reason : The point of intersection of parabola with the axis is called the vertex of the parabola.

Question. Assertion : The length of major and minor axes of the ellipse 5x² + 9y2 – 54y + 36 = 0 are 6 and 10, respectively.
Reason : The equation 5x² + 9y² – 54y + 36 = 0 can be expressed as 5x² + 9(y – 3)² = 45.

Question. Assertion : If the equation of standard parabola has a term y², then the axis of symmetry is along the x-axis.
Reason : If the equation of standard parabola has a term x2, then the axis of symmetry is along the x-axis.

Question. Assertion : The sum of focal distances of a point on the ellipse 9x² + 4y² – 18x – 24y + 9 = 0 is 4.
Reason : The equation 9x² + 4 y² – 18x – 24y + 9 = 0 can be expressed as 9(x – 1)2 + 4(y – 3)2 = 36.