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

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Questions
1 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)
2 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
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3 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)
4 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
5 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
6 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)
7 If (a, b) is the mid point of a chord passing through the vertex of the parabola y² = 4x, then
A a = 2b
B 2a = b
C a² = 2b
D 2a = b²

Answer:2a = b²
8 A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 meter and the distance between the flag posts is 8 meter. The equation of posts traced by the man is
A x²/9 + y²/5 = 1
B x²/9 + y2 /25 = 1
C x²/5 + y²/9 = 1
D x²/25 + y²/9 = 1

Answer:x²/25 + y²/9 = 1
9 The radius of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is?
A √57/4
B √77/4
C √77/2
D √87/4

Answer:√77/2
10 The locus of the point from which the tangent to the circles x² + y² – 4 = 0 and x² + y² – 8x + 15 = 0 are equal is given by the equation
A 8x + 19 = 0
B 8x – 19 = 0
C 4x – 19 = 0
D 4x + 19 = 0

Answer:8x – 19 = 0
11 The equation of a hyperbola with foci on the x-axis is
A x²/a² + y²/b² = 1
B x²/a² – y²/b² = 1
C x² + y² = (a² + b²)
D x² – y² = (a² + b²)

Answer:x²/a² – y²/b² = 1
12 At what point of the parabola x² = 9y is the abscissa three times that of ordinate
A (1, 1)
B (3, 1)
C (-3, 1)
D (-3, -3)

Answer:(3, 1)
13 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)
14 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
15 In an ellipse, the distance between its foci is 6 and its minor axis is 8 then its eccentricity is
A 4/5
B 1/√52
C 3/5
D 1/2

Answer:3/5
16 The perpendicular distance from the point (3, -4) to the line 3x – 4y + 10 = 0
A 7
B 8
C 9
D 10

Answer:7
17 The equation of parabola whose focus is (3, 0) and directrix is 3x + 4y = 1 is
A 16x² – 9y² – 24xy – 144x + 8y + 224 = 0
B 16x² + 9y² – 24xy – 144x + 8y – 224 = 0
C 16x² + 9y² – 24xy – 144x – 8y + 224 = 0
D 16x² + 9y² – 24xy – 144x + 8y + 224 = 0

Answer:16x² + 9y² – 24xy – 144x + 8y + 224 = 0
18 The parametric representation (2 + t², 2t + 1) represents
A a parabola
B a hyperbola
C an ellipse
D a circle

Answer:a parabola
19 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
20 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

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