Class 11 Maths Chapter 11 Conic Sections Questions and Answers

Questions

1 The length of the latus rectum of x² = 9y is equal to _______.

A 3 units

B 9/4 units

C 9 units

D -3 units

View Answer

Answer:9 units

2 (x²/9)+(y²/25) = 1 represents a vertical ellipse.

A True

B False

View Answer

Answer:True

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3 The equation of the directrix of the parabola y² = 16x is _______.

A 4

B -4

C 16

D -16

View Answer

Answer:-4

4 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

View Answer

Answer:1

5 The equation of common tangents to the curves x² + 4 y² = 8 and y² = 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

View Answer

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

6 The line y = x – 1 touches the ellipse 3 x² + 4 y² = 12, at

A (1/2, –1/2)

B (3, 2)

C (–1, –2)

D None of these

View Answer

Answer:None of these

7 Equation of the ellipse whose axes are co–ordinate axes and whose length of latus rectum, and eccentricity are equal and equal to ½ each is

A 6 x² + 12 yx² = 1

B 12 xx² + 6 yx² = 1

C 3 xx² + 12 yx² = 1

D 9 xx² + 12 yx² = 1

View Answer

Answer:9 xx² + 12 yx² = 1

8 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)

View Answer

Answer:(–1, 6)

9 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)

View Answer

Answer:(–1, 2) and (–1, –6)

10 The area of the triangle formed by the points on the ellipse 25x² + 16y² = 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

View Answer

Answer:20 sq. units

11 The general equation of second order ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents an ellipse if (Δ = abc + 2fgh - af² - bg² - ch² )

A Δ ≠ 0 and h² < ab

B Δ ≠ 0 and h² > ab

C Δ ≠ 0 and h² ≠ ab

D Δ ≠ 0 and h² = ab

View Answer

Answer:Δ ≠ 0 and h² < ab

12 The center of the circle 4x²+4y²-8x+12y-25=0 is ?

A (2,-3)

B (-2,3)

C (-4,6)

D (4,-6)

View Answer

Answer:(2,-3)

13 The focus of parabola y² = 8x is

A (-2, 0)

B focus and the vertex

C (0, 2)

D (0, -2)

View Answer

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

View Answer

Answer:the focus

15 The length of latus rectum of the ellipse x² /36 + y² /49 = 1 is

A 49/6

B 98/6

C 36/7

D 72/7

View Answer

Answer:72/7

16 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

View Answer

Answer:12y = x² + 4x + 16

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

A x² /12 + y² /16 = 1

B x² /16 + y² /12 = 1

C x² /4 + y² /12 = 1

D x² /12 + y² /4 = 1

View Answer

Answer:x² /16 + y² /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

View Answer

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 y² = 9x

B y² = 9x/2

C y² = 2x

D y² = 2x/9

View Answer

Answer:y² = 9x/2

20 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 x² + y² = 9

B x² -6x + 6y + y² = 0

C x² - 6y + y² = 0

D x² - 6x + y² = 0

View Answer

Answer:x² - 6x + y² = 0

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