NCERT Solutions for class 11 Maths | Chapter 11 - Conic Sections

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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

Answer:9 units
2 (x2/9)+(y2/25) = 1 represents a vertical ellipse.
A True
B False

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

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

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

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

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

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)

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)

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

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

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)

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)

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 latus rectum of the ellipse x2 /36 + y2 /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 = x2 + 4x + 16
B 12y = x2 + 4x + 16
C 12y = x2 + 4x
D 12y = x2 + 4x + 8

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

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

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

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

Answer:x2 - 6x + y2 = 0

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