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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 radius of the circumcircle of the P R S is

Options

  1. A5
  2. B3 3
  3. C3 2
  4. D2 3

Correct answer

B. 3 3

Step-by-step solution

Equation of circumcircle of P R S is (x+1)(x-9)+y^2+ y=0 It will pass through (1,2 2 ) , then aligned -16+8+ 2 2 & =0 & = 8 2 2 =2 2 aligned Equation of circumcircle is x^2+y^2-8 x+2 2 y-9=0 Hence, its radius is 3 3 . ALITER Let array ll Let & P S R= & = 2 2 2 3 & P R=6 2 =2 R array = 2 2 2 3 R=3 3 .

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