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JEE Advanced2007MathematicsParabolaActual

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the X -axis at R and tangents to the parabola at P and Q intersect the X -axis at S . Question: The ratio of the areas of the P Q S and P Q R is

Options

  1. A1: 2
  2. B1: 2
  3. C1: 4
  4. D1: 8

Correct answer

C. 1: 4

Step-by-step solution

Coordinates of P and Q are (1,2 2 ) and (1,-2 2 ) . Area of P Q R= 1 2 4 2 8=16 2 Area of P Q S= 1 2 4 2 2=4 2 Ratio of area of P Q S and P Q R is 1: 4 .

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