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 lngth of the common chord of the parabolas \({y^2} = x\) and \({x^2} = y\) is
  • A
    1
  • B
    \(\sqrt 2 \)
    Correct
  • C
    none of these
  • D
    \(4\sqrt 2 \)
2
The number of points on X-axis which are at a distance c units (c \(< \)3) from ( 2, 3) is
  • A
    1
  • B
    2
  • C
    0
    Correct
  • D
    3
3
The eccentricity of the conic \(9{x^2} - 16{y^2} = 144\) is
  • A
    \({4 \over 5}\)
  • B
    \({4 \over 3}\)
  • C
    \({5 \over 4}\)
    Correct
  • D
    \(\sqrt 7 \)
4
The eccentricity of \(3{x^2} + 4{y^2} = 24\) is
  • A
    \({1 \over 2}\)
    Correct
  • B
    \({1 \over 4}\)
  • C
    \(\sqrt {{7 \over 4}} \)
  • D
    \({7 \over 4}\)
5
The angle between the tangents drawn from the origin to the circle = \({(x - 7)^2} + {(y + 1)^2} = 25\) is
  • A
    \({\pi \over 3}\)
  • B
    \({\pi \over 2}\)
    Correct
  • C
    \({\pi \over 6}\)
  • D
    \({\pi \over 8}\)
6
The line y = mx + 1 is a tangent to the parabola \({y^2} = 4x\) if m =
  • A
    4
  • B
    2
  • C
    3
  • D
    1
    Correct
7
The equation \({x^2} - 7xy + 12{y^2} = 0\) represents a
  • A
    pair of non-perpendicular intersecting straight lines
    Correct
  • B
    circle
  • C
    pair of perpendicular straight lines
  • D
    pair of parallel straight lines
8
The equation \({y^2} - {x^2} + 2x - 1 = 0\) represents
  • A
    an ellipse
  • B
    a pair of straight lines
    Correct
  • C
    a circle
  • D
    an ellipse
9
The length of latus rectum of an ellipse is one-third of its major axis. Its eccentricity would be
  • A
    \({1 \over {\sqrt 3 }}\)
  • B
    \({2 \over 3}\)
  • C
    \(\sqrt {{2 \over 3}} \)
    Correct
  • D
    \({1 \over {\sqrt 2 }}\)
10
Three normals to the parabola \({y^2} = x\) are drawn through a point (c, 0) then
  • A
    none of these
  • B
    \(c = {1 \over 2}\)
  • C
    \(c = {1 \over 4}\)
  • D
    \(c > {1 \over 2}\)
    Correct
11
S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
  • A
    \({2 \over 3}\)
  • B
    \({1 \over 2}\)
    Correct
  • C
    \({1 \over 3}\)
  • D
    \({1 \over 4}\)
12
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle \({x^2} + {y^2} = 9\) is
  • A
    \(\left( {{1 \over 2},{3 \over 2}} \right)\)
  • B
    \(\left( {{1 \over 2},\;{1 \over 2}} \right)\)
  • C
    \(\left( {{1 \over 2}, - \;\sqrt 2 } \right)\)
  • D
    \(\left( {{1 \over 2}, - \sqrt 2 } \right)\)
    Correct
13
The number of tangents to the circle \({x^2} + {y^2} - 2x + 4y = 0\) through the point ( - 1, 2) is
  • A
    2
    Correct
  • B
    none of these
  • C
    1
  • D
    0
14
The slope of the tangent at the point (h, h) of the circle \({x^2} + {y^2} = {a^2}\) is
  • A
    0
  • B
    depends upon h
  • C
    -1
    Correct
  • D
    0
15
The equation of the normal to the parabola \({y^2} = 8\)x having slope 1 is
  • A
    x – y + 6 = 0
  • B
    x + y – 6 = 0
  • C
    x + y + 6 = 0
  • D
    x – y – 6 = 0
    Correct