Conic Sections CBSE Questions & Answers

Conic Sections

This is Mathematics Class 11 Conic Sections CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Which of the following lines is a normal to the circle \({(x - 1)^2} + {(y - 2)^2} = 10\)
  • A
    x + y = 3
    Correct
  • B
    x +2y = 10
  • C
    ( x – 1) = ( y – 2) = 10
  • D
    2x + y = 3 ?
2
A circle with its centre on the line y = x + 1 is drawn to pass through the origin and touch the line y = x + 2. The centre of the circle is
  • A
    (-1, 2)
  • B
    \(\left( {{1 \over 2},{1 \over 2}} \right)\)
  • C
    (- 1, 0)
  • D
    \(\left( { - {1 \over 2},{1 \over 2}} \right)\)
    Correct
3
Four distinct points \((2\lambda ,3\lambda ),(1,0),(0,1)\) and (0, 0) lie on a circle for
  • A
    0 \(<\) \(\lambda \)\(<\)1
  • B
    none of these
  • C
    only one value of \(\lambda \)
    Correct
  • D
    \(\lambda \)\(<\) 0
4
The locus of the point of intersection of the lines x cos \(\alpha \) + y sin \(\alpha = a\) and x sin \(\alpha \) - y cos \(\alpha \) = b is
  • A
    a circle
    Correct
  • B
    none of these.
  • C
    an ellipse
  • D
    a straight line
5
The line y = m x + c is a normal to the circle \({x^2} + {y^2} + 2gx + 2fy + c = 0\;if\)
  • A
    none of these
  • B
    mg \( \ne \) c + f
  • C
    mg = c + f
    Correct
  • D
    c = 0
6
The line 3x – 4y = 0
  • A
    does not pass through the origin
  • B
    is a tangent to the circle \({x^2} + {y^2} = 25\)
  • C
    is a normal to the circle \({x^2} + {y^2} = 25\)
    Correct
  • D
    does not meet the circle \({x^2} + {y^2} = 25\)
7
The equations x = a cos \(\theta \) + b sin \(\theta \) , and \(y = a\sin \theta - b\cos \theta \) , 0 \( \le \) \(\theta \) \( \le \) 2 \(\pi \) represent
  • A
    an ellipse
  • B
    a parabola
  • C
    a circle
    Correct
  • D
    a hyperbola
8
The number of points which have the same power w.r.t. two (different) concentric circles is
  • A
    two
  • B
    infinitely many
  • C
    one
  • D
    none of these
    Correct
9
A circle passes through (0, 0) ( a, 0), (0, b). The coordinates of its centre are
  • A
    (- a, - b)
  • B
    \(\left( {{a \over 2},{b \over 2}} \right)\)
    Correct
  • C
    (a, b)
  • D
    (b, a)
10
The focus of the parabola \({x^2} - 8x + 2y + 7 = 0\) is
  • A
    \(\left( {0, - {1 \over 2}} \right)\)
  • B
    (4, 4)
    Correct
  • C
    \(\left( { - 4, - {9 \over 2}} \right)\)
  • D
    \(\left( {4,{9 \over 2}} \right)\)
11
The radius of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9}\) \({{{x^2}} \over {16}} + {{{y^2}} \over 9}\) =1 and having its centre at (0, 3) is
  • A
    \(\sqrt {12} \)
  • B
    \({7 \over 2}\)
  • C
    4
    Correct
  • D
    3
12
The line y = c is a tangent to the parabola \({7 \over 2}\) if c is equal to
  • A
    2 a
  • B
    0
  • C
    a
  • D
    none of these
    Correct
13
The equation \(2{x^2} + 3{y^2} - 8x - 18y + 35 = \lambda \) Represents
  • A
    an ellipse if \(\lambda < 0\)
  • B
    a point if \(\lambda = 0\)
    Correct
  • C
    the empty set if \(\lambda > 0\)
  • D
    a circle for all \(\lambda \)
14
The locus of a variable point whose distance from the point ( 2, 0) is \({2 \over 3}\) times its distance from the line \(x = {9 \over 2}\) is
  • A
    a parabola
  • B
    a circle
  • C
    an ellipse
    Correct
  • D
    a hyperbola
15
The axis of the parabola \(9{y^2} - 16x - 12y - 57 = 0\) is
  • A
    none of these
  • B
    y = 0
  • C
    16 x + 61 = 0
  • D
    3 y = 2
    Correct