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AP EAMCET202423 May 2024Morning ShiftMathematicsCircleActual

Consider the point P( , ) on the line 2 x+y=1 . If the P and (3,2) are conjugate points with respect to the circle x^2+y^2=4 , then + =

Options

  1. A3
  2. B-1
  3. C-5
  4. D7

Correct answer

A. 3

Step-by-step solution

Polar of point (3,2) w.r.t. circle x^2+y^2=4 is T₁=0 3 x+2 y=4 Since, (3,2) and P( , ) are conjugate point. So, polar of (3,2) passes through P( , ) 3 +2 =4 ...(i) Also, P( , ) lies on 2 x+y=1 2 + =1 ...(ii) Solving (i) and (ii), =-2, =5 + =-2+5=3 .

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