These Conic Sections Class 11 MCQ and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Conic Sections Class 11 MCQ and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Conic Sections Class 11 MCQ and Answers

1. Equation of the ellipse whose axes are coordinate axes and whose length of latus rectum, and eccentricity are equal and equal to ½ each is

(A) 6 x^{2} + 12 yx^{2} = 1

(B) 12 xx^{2} + 6 yx^{2} = 1

(C) 3 xx^{2} + 12 yx^{2} = 1

(D) 9 xx^{2} + 12 yx^{2} = 1

**Answer:** 9 xx^{2} + 12 yx^{2} = 1

2. The equation 3 (x + y – 5)^{2} + 2 (x – y + 7)^{2} = 6 represents an ellipse, whose centre is

(A) (–1, 6)

(B) (6, –1)

(C) (1, –6)

(D) (–6, 1)

**Answer:** (–1, 6)

3. If a parabolic reflector is 20 cm in diameter and 5 cm deep then the focus of parabolic reflector is

(A) (0 0)

(B) (0, 5)

(C) (5, 0)

(D) (5, 5)

**Answer:** (5, 0)

4. If the length of the tangent from the origin to the circle centered at (2, 3) is 2 then the equation of the circle is

(A) (x + 2)² + (y – 3)² = 3²

(B) (x – 2)² + (y + 3)² = 3²

(C) (x – 2)² + (y – 3)² = 3²

(D) (x + 2)² + (y + 3)² = 3²

**Answer:** (x – 2)² + (y – 3)² = 3²

5. The center of the ellipse (x + y – 2)² /9 + (x – y)² /16 = 1 is

(A) (0, 0)

(B) (0, 1)

(C) (1, 0)

(D) (1, 1)

**Answer:** (1, 1)

6. The number of tangents that can be drawn from (1, 2) to x² + y² = 5 is

(A) 0

(B) 1

(C) 2

(D) More than 2

**Answer:** 1

7. The equation of parabola with vertex (-2, 1) and focus (-2, 4) is

(A) 10y = x² + 4x + 16

(B) 12y = x² + 4x + 16

(C) 12y = x² + 4x

(D) 12y = x² + 4x + 8

**Answer:** 12y = x² + 4x + 16

8. The parametric coordinate of any point of the parabola y² = 4ax is

(A) (-at², -2at)

(B) (-at², 2at)

(C) (a sin²t, -2a sin t)

(D) (a sin t, -2a sin t)

**Answer:** (a sin²t, -2a sin t)

9. The equation of the parabola with vertex at (0, 0) and focus at ((-5/2), 0) is _____________.

(A) y^{2} = -10x

(B) y^{2} = 10x

(C) x^{2} = -10y

(D) x^{2} = 10y

**Answer:** y^{2} = -10x

10. Choose the false statement.

(A) x^{2} = 4 ay represents the upward parabola.

(B) x^{2} = -4 ay represents downward parabola.

(C) y^{2} = 4 ax represents the right handed parabola.

(D) y^{2} = -4 ax represents the right handed parabola.

**Answer:** y^{2} = -4 ax represents the right handed parabola.

11. A parabolic reflector is 10 cm in diameter. It’s depth is 2.5 cm. The focus will be _______.

(A) (2.5, 0)

(B) (0, 2.5)

(C) (5, 0)

(D) (0, 5)

**Answer:** (2.5, 0)

12. The equation of the circle having radius 3 units and which touches the y-axis at the origin and lies in the 1st and 4thquadrant is ____.

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

(B) x^{2} -6x + 6y + y^{2} = 0

(C) x^{2} – 6y + y^{2} = 0

(D) x^{2} – 6x + y^{2} = 0

**Answer:** x^{2} – 6x + y^{2} = 0

13. The area of the circle is 154 square units. The equation of 2 of its diameters are x + y = 6 and x + 2y = 4. Then, the equation of the circle is ____.

(A) x^{2} + y^{2} – 16x + 2y + 49 = 0

(B) x^{2} + y^{2} – 16x + 2y + 19 = 0

(C) x^{2} + y^{2} – 16x + 16y + 19 = 0

(D) x^{2} + y^{2} – 2x + 2y + 19 = 0

**Answer:** x^{2} + y^{2} – 16x + 2y + 19 = 0

14. The equation of the directrix of x^{2} = -8y is _____.

(A) -8

(B) 8

(C) 2

(D) -2

**Answer:** 2

15. The eccentricity of the ellipse is ___________

(A) 0 < e < 1

(B) -1 < e < 0

(C) -1 < e < 1

(D) -1 < e < ∞

**Answer:** 0 < e < 1

16. A ray of light moving parallel to the x-axis gets reflected from a parabolic mirror whose equation is (y – 2)2 = 4(x + 1). Then, after reflection, the ray must pass through the point ___________.

(A) (2, -1)

(B) (0, 2)

(C) (-1, 2)

(D) (1, 0)

**Answer:** (0, 2)

17. The co-ordinates of the foci of an ellipse are (4, 0), (-4, 0). It represents a ______.

(A) horizontal ellipse

(B) vertical ellipse

(C) nil

(D) nil

**Answer:** horizontal ellipse

18. Choose the false statement.

(A) x2 = 4 ay represents the upward parabola.

(B) x2 = -4 ay represents downward parabola.

(C) y2 = 4 ax represents the right handed parabola.

(D) y2 = -4 ax represents the right handed parabola.

**Answer:** y2 = -4 ax represents the right handed parabola.

19. If one end point of the diameter of the circle x2 + y2 – 8x – 4y + c = 0 is (-3, 2), then the other end of the diameter of the circle is ____.

(A) (3, 2)

(B) (0, 0)

(C) (11, 2)

(D) (-11, 2)

**Answer:** (11, 2)

20. A circle of radius 5 units has its centre on the positive x-axis. If the circle passes through the point (2, 3), then the centre of the circle is ____.

(A) (5, 0)

(B) (2, 0)

(C) (6, 0)

(D) (7, 0)

**Answer:** (6, 0)