Conic Sections — Class 11 MCQs with Answers

Conic Sections — important questions & MCQs with answers (Class 11 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Equation of circle centre (0,0), radius r:

   A.x²+y²=r²✓ Correct

   B.x²−y²=r²

   C.x+y=r

   D.x²+y² = r

   Answer: A. x²+y²=r²

   Explanation: Every point stays a fixed distance r from the centre, and squaring that distance gives x²+y²=r² — squaring both sides is the step everyone forgets, which is why x²+y²=r (missing the square on r) tempts.

2. Q2Easy

   A circle is the set of all points:

   A.Equidistant from a fixed point✓ Correct

   B.On a straight line

   C.From a parabola

   D.Of finite distance from origin

   Answer: A. Equidistant from a fixed point

   Explanation: A circle is the locus of points at a fixed distance (the radius) from one fixed point (the centre) — an ellipse instead keeps the SUM of distances to two foci constant, a definition students often blend with this one.

3. Q3Easy

   A parabola is the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). Eccentricity e =

   A.2

   B.0

   C.1✓ Correct

   D.Variable

   Answer: C. 1

   Explanation: By definition every point on a parabola is EQUIDISTANT from the focus and directrix, so the ratio of these distances is exactly 1 — e=1 makes a parabola, e<1 an ellipse and e>1 a hyperbola.

4. Q4Easy

   An ellipse is the locus of points whose sum of distances from two fixed points (foci) is:

   A.Equal to distance between foci

   B.Variable

   C.Constant✓ Correct

   D.Zero

   Answer: C. Constant

   Explanation: An ellipse is defined by keeping the SUM of distances to the two foci constant (equal to 2a) — a hyperbola instead keeps the DIFFERENCE constant, and swapping sum for difference is the classic mix-up.

5. Q5Easy

   Hyperbola: locus of points whose absolute difference of distances from two fixed points (foci) is:

   A.Zero

   B.Variable

   C.Constant✓ Correct

   D.Equal

   Answer: C. Constant

   Explanation: A hyperbola is defined by keeping the absolute DIFFERENCE of distances to the two foci constant (equal to 2a) — swapping this for the SUM, which defines an ellipse, is the common confusion.

6. Q6Easy

   Conic section is formed by intersecting a plane with a:

   A.Double cone✓ Correct

   B.Cylinder

   C.Sphere

   D.Cube

   Answer: A. Double cone

   Explanation: Slicing a double (two-nappe) cone with a plane at different angles produces the circle, ellipse, parabola and hyperbola — a cylinder or sphere gives only circles, never the full family.

7. Q7Medium

   For parabola y²=8x, focus is at:

   A.(0,2)

   B.(2,0)✓ Correct

   C.(8,0)

   D.(4,0)

   Answer: B. (2,0)

   Explanation: Match y²=8x to y²=4ax: 4a=8 gives a=2, so the focus sits at (a,0)=(2,0) — confusing focus (a,0) with directrix x=−a would wrongly give a point at (−2,0).

8. Q8Medium

   Centre and radius of circle x² + y² − 6x + 4y − 12 = 0:

   A.(3, −2), 5✓ Correct

   B.(−3, 2), 5

   C.(3, 2), 12

   D.(6, −4), 12

   Answer: A. (3, −2), 5

   Explanation: Complete the square: x²−6x becomes (x−3)²−9 and y²+4y becomes (y+2)²−4, so the equation becomes (x−3)²+(y+2)²=25 — centre (3,−2), radius 5. Missing the sign flip on the y-term gives the wrong centre (−3,2).

9. Q9Medium

   Focus of parabola y² = 12x:

   A.(0, 3)

   B.(3, 0)✓ Correct

   C.(−3, 0)

   D.(0, −3)

   Answer: B. (3, 0)

   Explanation: 4a=12 gives a=3, and the focus of y²=4ax sits at (a,0)=(3,0) — mixing up focus and directrix would instead give x=−3.

10. Q10Medium

    Eccentricity of ellipse x²/25 + y²/9 = 1:

    A.3/5

    B.4/5✓ Correct

    C.5/4

    D.9/25

    Answer: B. 4/5

    Explanation: a²=25 and b²=9 give c=√(a²−b²)=√16=4, so e=c/a=4/5 — using a²+b² instead, the hyperbola formula, would wrongly give e>1.

11. Q11Medium

    Foci of hyperbola x²/9 − y²/16 = 1:

    A.(±4, 0)

    B.(0, ±5)

    C.(±3, 0)

    D.(±5, 0)✓ Correct

    Answer: D. (±5, 0)

    Explanation: For a hyperbola c=√(a²+b²)=√(9+16)=5, so the foci sit at (±5,0) — this PLUS sign (not the ellipse's minus) is what pushes c past a, giving e>1.

12. Q12Hard

    Radius of circle x² + y² + 8x − 10y + 5 = 0:

    A.6✓ Correct

    B.√41

    C.8

    D.√(8² + 10² − 5)

    Answer: A. 6

    Explanation: Complete the square: r² = (8/2)² + (10/2)² − 5 = 16 + 25 − 5 = 36, so r = 6. The general form x²+y²+2gx+2fy+c=0 gives r²=g²+f²−c using HALF the linear coefficients; feeding in 8 and 10 unhalved gives the tempting √(8²+10²−5).

13. Q13Hard

    Vertex of parabola y² + 4x − 6y + 13 = 0:

    A.(1, −3)

    B.(−1, 3)✓ Correct

    C.(0, 0)

    D.(2, 4)

    Answer: B. (−1, 3)

    Explanation: Complete the square in y: y²−6y+13=(y−3)²+4, so the equation becomes (y−3)²=−4(x+1) — a parabola opening left with vertex (−1,3); reading the vertex straight off the constants without completing the square gives the wrong point (1,−3).

14. Q14Hard

    Length of latus rectum of ellipse x²/16 + y²/9 = 1:

    A.6

    B.18

    C.16/3

    D.9/2✓ Correct

    Answer: D. 9/2

    Explanation: Latus rectum of an ellipse is 2b²/a=2(9)/4=18/4=9/2 — using 2a²/b or forgetting to divide by a (giving 18) are the usual slips.

Conic Sections — FAQs

More Class 11 Mathematics chapters

• 01Sets
• 02Relations and Functions
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 06Linear Inequalities

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