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AP EAMCET2001MathematicsCircle

If the polar of a point on the circle x^2+y^2=p^2 with respect to the circle x^2+y^2=q^2 touches the circle x^2+y^2=r^2 , then p, q, r are in

Options

  1. AAP
  2. BGP
  3. CHP
  4. DAGP

Correct answer

B. GP

Step-by-step solution

We have, polar equation with respect to x^2+y^2=p^2 is x x₁+y y₁=q^2 This equation touches the circle x^2+y^2-r^2=0 aligned & Then, r= 0+0-q^2 x₁^2+y₁^2 & -q^2=r x₁^2+y₁^2 -q^2=r p^2 & -q^2= r p q^2=p r & aligned Thus p, q and r in GP.

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