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
If the line 2x – y + \(\lambda \) = 0 is a diameter of the circle \({x^2} + {y^2} + 6x - 6y + 5 = 0\) then \(\lambda \) =
  • A
    9
    Correct
  • B
    3
  • C
    6
  • D
    12
2
Length of common chord of the circles \({x^2} + {y^2} + 2x + 6y = 0\) and \({x^2} + {y^2} - 4x - 2y - 6 = 0\) is
  • A
    \({1 \over 5}\sqrt {106} \)
  • B
    \(\sqrt {106} \)
  • C
    \({2 \over 5}\sqrt {106} \)
    Correct
  • D
    \(2\sqrt {106} \)
3
The circles \({x^2} + {y^2} + 6x + 6y = 0\) and \({x^2} + {y^2} - 12x - 12y = 0\)
  • A
    intersect in two points
  • B
    touch each other externally
    Correct
  • C
    cut orthogonally
  • D
    touch each other internally
4
The equation \({x^2} + {y^2} = 0\) represents
  • A
    a circle
  • B
    a degenerate circle
    Correct
  • C
    an empty set
  • D
    a straight line
5
The equation 3 \(({x^2} + {y^2}) + 5x - 7y - 2 = 0\) represents
  • A
    a pair of straight lines
  • B
    a circle
    Correct
  • C
    an empty set
  • D
    a degenerate circle
6
Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is
  • A
    (2, 0)
  • B
    ( 3, 2)
    Correct
  • C
    (0, 3)
  • D
    (3, 0)
7
If \({({x^2} - a)^2} + {(y - b)^2} = {c^2}\) represents a circle, then
  • A
    a = 0
  • B
    b = 0
  • C
    c \( \ne \) 0
    Correct
  • D
    a = b = 0
8
The length of the chord joining the point ( 4 cos \(\theta \), 4 sin \(\theta \)) and 4 ( cos(\(\theta \)+\({60^o}\)), 4 sin(\(\theta \) + \({60^o}\))) of the circle \({x^2} + {y^2} = 16\) is
  • A
    2
  • B
    8
  • C
    16
  • D
    4
    Correct
9
Two perpendicular tangents to the circle \({x^2} + {y^2} = {r^2}\) meet at P. The locus of P is
  • A
    \({x^2} + {y^2} = 2\;{r^2}\)
    Correct
  • B
    x + y = r
  • C
    \({x^2} + {y^2} = {{{r^2}} \over 2}\)
  • D
    \({x^2} + {y^2} = 4\;{r^2}\)
10
The number of tangents to the circle \({x^2} + {y^2} - 8x - 6y + 9 = 0,\) which pass through the point ( 3, - 2), is
  • A
    0
  • B
    1
  • C
    none of these
  • D
    2
    Correct
11
The value of k, such that the equation = \(2{x^2} + 2{y^2} - 6x + 8y + k = 0\) represents a point circle, is
  • A
    0
  • B
    25
  • C
    \({{25} \over 2}\)
    Correct
  • D
    \( - {{25} \over 2}\)
12
The equation \(a{x^2} + b{y^2} + 2hxy + 2gx + 2fy + c = 0\) represents a circle only if
  • A
    \(a = b \ne 0,h = 0,{g^2} + {f^2} - ac > 0\)
    Correct
  • B
    a = b \( \ne \) 0, h = 0
  • C
    a = b , h = 0
  • D
    a = b \( \ne \) 0, h = 0, \({g^2} + {f^2} - c > 0\)
13
\({x^2} + {y^2} - 6x + 8y - 11 = 0\) is a circle. The points (0, 0) and ( 1, 8) lie
  • A
    both outside the circle
  • B
    one outside the circle and one inside
    Correct
  • C
    one on the circle and the other outside
  • D
    both inside the circle
14
The length of tangent from the point ( 2, - 3) to the circle \(2{x^2} + 2{y^2} = 1\) is
  • A
    5
  • B
    - 5
  • C
    \({5 \over {\sqrt 2 }}\)
    Correct
  • D
    \( - {5 \over {\sqrt 2 }}\)
15
Which one of the following lines is farthest from the centre of the circle \({x^2} + {y^2} = 10?\)
  • A
    3 x + 4 y – 15 = 0
  • B
    x + y = 1
  • C
    \(x + \sqrt 3 \;y + 7 = 0\)
    Correct
  • D
    12x + 5 y + 26 = 0