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
The equation of the tangent to the conic \({x^2} - {y^2} - 8x + 2y + 11 = 0\) at (2, 1) is
  • A
    x – 2 = 0
    Correct
  • B
    x + y + 1 = 0
  • C
    2 x + 1 = 0
  • D
    x – 2 = 0
2
In an ellipse the distance between its foci is 6 and its minor axis is 8 ; the eccentricity of the ellipse is
  • A
    \({3 \over 5}\)
    Correct
  • B
    \({1 \over 2}\)
  • C
    \({3 \over 5}\)
  • D
    \({1 \over {\sqrt {52} }}\)
3
If the length of the major axis of an ellipse is three times the length of its minor axis, its eccentricity is
  • A
    \({{2\sqrt 2 } \over 3}\)
    Correct
  • B
    \({1 \over {\sqrt 2 }}\)
  • C
    \({1 \over 3}\)
  • D
    \({1 \over {\sqrt 3 }}\)
4
At what point on the parabola \({y^2} = 4x,\) the normal makes equal angles with the axes ?
  • A
    (9, 6)
  • B
    (1, - 2)
    Correct
  • C
    (4, -4)
  • D
    (4, 4)
5
The number of common tangents to the circles \({x^2} + {y^2} - x = 0,{x^2} + {y^2} + x = 0\) is
  • A
    4
  • B
    1
  • C
    3
    Correct
  • D
    2
6
The locus of a point which moves so that its distance from a fixed point, called focus, bears a constant ratio, which is less than unity, to its distance from a fixed line, called the directrix is called
  • A
    an ellipse
    Correct
  • B
    a hyperbola
  • C
    a circle
  • D
    a parabola
7
The axis of the parabola \(9{y^2} - 16x - 12y - 57 = 0\) is
  • A
    y = 3
  • B
    x + 3y = 3
  • C
    3 y = 2
    Correct
  • D
    2 x = 3
8
Consider a circle with its centre lying on the focus of the parabola \({y^2} = 2\) px such that it touches the directrix of the parabola, then a point of intersection of the circle and the parabola is
  • A
    \(\left( { - {p \over 2} - p} \right)\)
  • B
    \(\left( { - {p \over 2},p} \right)\)
  • C
    \(\left( {{p \over 2}, - p} \right)\)
  • D
    \(\left( {{p \over 2},p} \right)\)
    Correct
9
The straight line 3 x + 4 y = 20 and the circle \({x^2} + {y^2} = 16\)
  • A
    none of these
  • B
    touch each other
    Correct
  • C
    intersect in two distinct points
  • D
    neither touch nor intersect in two points
10
The equation \({x^2} + 3{y^2} - 9x + 2y + 1 = 0\) represents
  • A
    a hyperbola
  • B
    a parabola
  • C
    an ellipse
    Correct
  • D
    a circle
11
A bridge is in the shape of a semi-ellipse. It is 400 meters long and has a maximum height of 10 metres at the middle points. The height of the bridge at a point distant 80 meters from one end is
  • A
    4 metres
  • B
    8 metres
    Correct
  • C
    2 metres
  • D
    \(\sqrt {91} \) metres
12
The radius of the circle 3 x ( x – 2) + 3 y ( y + 1) = 4 is
  • A
    3
  • B
    \(\sqrt {{{15} \over 4}} \)
  • C
    \(\sqrt {{{31} \over {12}}} \)
    Correct
  • D
    2
13
If the angle between the lines joining the foci of an ellipse to an extremity of a minor axis is \({90^o}\) , then the eccentricity of the ellipse is
  • A
    \({1 \over 8}\)
  • B
    \({1 \over {\sqrt 2 }}\)
    Correct
  • C
    \({1 \over 4}\)
  • D
    \({1 \over {\sqrt 3 }}\)
14
The vertex of the parabola \({y^2} = 4\;a\) ( x + a) is
  • A
    (0, a)
  • B
    (- a, 0)
    Correct
  • C
    (a, 0)
  • D
    (0, 0)
15
If 3 x + y = 0 is a tangent to the circle which has its center at the point ( 2, - 1), then the equation of the other tangent to the circle from the origin is
  • A
    x + 3 y = 0
  • B
    x – 3 y = 0
    Correct
  • C
    3 x – y = 0
  • D
    x + 2 y = 0