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AP EAMCET202419 May 2024Evening ShiftMathematicsCircleActual

Let P be any point on the circle x^2+y^2=25 . Let L be the chord of contact of P with respect to the circle x^2+y^2= 9. The locus of the poles of the lines L with respect to the circle x^2+y^2=36 is

Options

  1. Ay^2=20 x
  2. Bx^2 9 + y^2 36 =1
  3. Cx^2+y^2=400
  4. Dx^2 25 - y^2 16 =1

Correct answer

C. x^2+y^2=400

Step-by-step solution

Let P(r, s) be point on circle x^2+y^2=25 r ^2+ s ^2=25...(i) Equation of chord of contact of P w.r.t. circle x^2+y^2=9 is L L : xr + ys -9=0...(ii) Poles of line L w.r.t. circle x^2+y^2=36 is ( h, k ) then xh + yk -36=0...(iii) Solving (ii) and (iii), we get substitute value of r and s in e^ n (i) h 4 =r, k 4 =s h^2 16 + k^2 16 =25 So required locus of pole is x^2+y^2=400 .

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