JEE Maths - Conic Sections

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Question - 1

The line 4x+3y-4 =0 divides the circumference of the circle centered at (5, 3), in the ratio 1 : 2. Then the equation of the circle is ____________ .

  • A \(x^{2}+y^{2}-10 x-6 y-66=0 \)
  • B \(x^{2}+y^{2}-10 x-6 y+100=0 \)
  • C \(x^{2}+y^{2}-10 x-6 y+66=0 \)
  • D \(x^{2}+y^{2}-10 x-6 y-100=0\)

Question - 2

Let A(- 4, 0) and B(4,0). Then the number of points C = (x, y) on the circle x2 + x2 = I 6 lying in first quadrant such that the area of the triangle whose vertices are A,.B and C is a integer is ____________ .

  • A 14
  • B 15
  • C 16
  • D None of these

Question - 3

If (α, β) is a point on the circle whose centre is on the x-axis and which touches the line x + y = 0 at (2,-2), then the greatest value of α is ____________ .

  • A \(4-\sqrt{2} \)
  • B 6
  • C \(4+2 \sqrt{2} \)
  • D \(4+\sqrt{2}\)

Question - 4

The set of values of  'c' so that the equations \(y=|x|+c and x^{2}+y^{2}-8|x|-9=0\) have no solution is _____________ .

  • A \((-\infty,-3) \cup(3, \infty) \)
  • B (3,3)
  • C \( (-\infty,-\sqrt{2}) \cup(5 \sqrt{2}, \infty) \)
  • D \((5 \sqrt{2}-4, \infty)\)

Question - 5

Tangents are drawn from O (origin) to touch the circle.\(x^{2}+y^{2}+2 g x+2 f y+c=0\) at points P and Q. The equation of the circle circumscribing triangle OPQ is ____________ .

  • A \(2 x^{2}+2 y^{2}+g x+f y=0 \)
  • B \(x^{2}+y^{2}+g x+f y=0 \)
  • C \(x^{2}+y^{2}+2 g x+2 f y=0 \)
  • D None of these

Question - 6

A ray of light incident at the point (-2,- 1) gets reflected from the tangent at (0, -1) to the circle The reflected ray touches the circle. The equation the line along which the incident ray moved, is _____________ .

  • A \(4 x-3 y+11=0 \)
  • B \(4 x+3 y+11=0 \)
  • C \(3 x+4 y+11=0 \)
  • D \(4 x+3 y+7=0\)

Question - 7

If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is ____________ .

  • A \(2 a x-2 b y-\left(a^{2}+b^{2}+4\right)=0 \)
  • B \(2 a x+2 b y-\left(a^{2}+b^{2}+4\right)=0 \)
  • C \(2 a x-2 b y+\left(a^{2}+b^{2}+4\right)=0 \)
  • D \(2 a x+2 b y+\left(a^{2}+b^{2}+4\right)=0\)

Question - 8

If the line y = mx+1 meets the circle \(x^{2}+y^{2}+3 x=0\) in two points equidistant from and on opposite sides of x-axis, then ____________ .

  • A \(3 m+2=0 \)
  • B \(3 m-2=0 \)
  • C \(2 m+3=0 \)
  • D \(2 m-3=0\)

Question - 9

The set of all real values of λ for which exactly two common tangents can be drawn to the circles \(x^{2}+y^{2}-4 x-4 y+6=0 \) and \(x^{2}+y^{2}-10 x-10 y+\lambda=0 \) is the interval ___________ .

  • A (12, 32)
  • B (18, 42)
  • C (12, 24)
  • D (18, 48)

Question - 10

A circle bisects the circumference of the circle \(x^{2}+y^{2}-2 y-3=0\) and touches the line x = y and the point (1, 1). Its radius is _____________ .

  • A \(\frac{3}{\sqrt{2}} \)
  • B \(\frac{9}{\sqrt{2}} \)
  • C \(4 \sqrt{2} \)
  • D \(3 \sqrt{2}\)
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