These Conic Sections Class 11 NCERT Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Conic Sections Class 11 NCERT Questions 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 NCERT Questions and Answers

1. A rod of length 12 CM moves with its and always touching the co-ordinate Axes. Then the equation of the locus of a point P on the road which is 3 cm from the end in contact with the x-axis is

(A) x²/81 + y²/9 = 1

(B) x²/9 + y²/81 = 1

(C) x²/169 + y²/9 = 1

(D) x²/9 + y²/169 = 1

**Answer:** x²/81 + y²/9 = 1

2. The line lx + my + n = 0 will touches the parabola y² = 4ax if

(A) ln = am²

(B) ln = am

(C) ln = a² m²

(D) ln = a² m

**Answer:** ln = am²

3. Foci of the ellipse; 25 (x + 1)^{2} +9(y +2)^{2} = 225, are<

(A) (–1, –2) and (–1, –6)

(B) (–2, 1) and (–2, 6)

(C) (–1, 2) and (–1, –6)

(D) (–1, 2) and (–1, –6)

**Answer:** (–1, 2) and (–1, –6)

4. The area of the triangle formed by the points on the ellipse 25x^{2} + 16y^{2} = 400 whose eccentric angles are p/2, p and 3p/2 is

(A) 10 sq. units

(B) 20 sq. units

(C) 30 sq. units

(D) 40 sq. units

**Answer:** 20 sq. units

5. The general equation of second order ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 represents an ellipse if (Δ = abc + 2fgh – af^{2} – bg^{2} – ch^{2} )

(A) Δ ≠ 0 and h^{2} < ab

(B) Δ ≠ 0 and h^{2} > ab

(C) Δ ≠ 0 and h^{2} ≠ ab

(D) Δ ≠ 0 and h^{2} = ab

**Answer:** Δ ≠ 0 and h^{2} < ab

6. The length of the latus rectum of x^{2} = 9y is equal to _______.

(A) 3 units

(B) 9/4 units

(C) 9 units

(D) -3 units

**Answer:** 9 units

7. (x^{2}/9)+(y^{2}/25) = 1 represents a vertical ellipse.

(A) True

(B) False

**Answer:** True

8. The equation of the directrix of the parabola y^{2} = 16x is _______.

(A) 4

(B) -4

(C) 16

(D) -16

**Answer:** -4

9. The focal distance of a point on the parabola y2 = 16x is 5. The abcissa of this point is _____.

(A) 1

(B) 4

(C) -1

(D) 5

**Answer:** 1

10. The equation of common tangents to the curves x^{2} + 4 y^{2} = 8 and y^{2} = 4 x are

(A) 2 y – x – 4 = 0 and 2 y + x + 4 = 0

(B) y – 2 x – 4 = 0 and y + 2 x + 4 = 0

(C) 2 y – x – 2 = 0 and 2 y + x + 2 = 0

(D) y – 2 x – 2 = 0 and y + 2 x + 2 = 0

**Answer:** 2 y – x – 4 = 0 and 2 y + x + 4 = 0

11. The line y = x – 1 touches the ellipse 3 x^{2} + 4 y^{2} = 12, at

(A) (1/2, –1/2)

(B) (3, 2)

(C) (–1, –2)

(D) None of these

**Answer:** None of these

12. The center of the circle 4x^{2}+4y^{2}-8x+12y-25=0 is ?

(A) (2,-3)

(B) (-2,3)

(C) (-4,6)

(D) (4,-6)

**Answer:** (2,-3)

13. The focus of parabola y^{2} = 8x is

(A) (-2, 0)

(B) focus and the vertex

(C) (0, 2)

(D) (0, -2)

**Answer:** (-2, 0)

14. A chord of the parabola is a focal chord if it passes through ____

(A) the center

(B) the focus

(C) the vertex

(D) None of these

**Answer:** the focus

15. The length of the latus rectum of the ellipse x^{2} /36 + y^{2} /49 = 1 is

(A) 49/6

(B) 98/6

(C) 36/7

(D) 72/7

**Answer:** 72/7

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

(A) 10y = x^{2} + 4x + 16

(B) 12y = x^{2} + 4x + 16

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

(D) 12y = x^{2} + 4x + 8

**Answer:** 12y = x^{2} + 4x + 16

17. The foci of an ellipse are (±2, 0) and its eccentricity is 1/2 then its equation is

(A) x^{2} /12 + y^{2} /16 = 1

(B) x^{2} /16 + y^{2} /12 = 1

(C) x^{2} /4 + y^{2} /12 = 1

(D) x^{2} /12 + y^{2} /4 = 1

**Answer:** x^{2} /16 + y^{2} /12 = 1

18. If a chord the circle x2 + y2 = 8 makes equal intercepts of lenghtsa on the coordinate axes, then

(A) |a| < 8

(B) |a| < 4

(C) |a| > 4

(D) |a| > 8

**Answer:** |a| < 4

19. The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is

(A) y^{2} = 9x

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

(C) y^{2} = 2x

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

**Answer:** y^{2} = 9x/2

20. The equation of the circle having radius of 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