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AP EAMCET20227 Jul 2022Morning ShiftMathematicsCircleActual

The equation of circle passing through (0,0) and cutting orthogonally the circles x^2+y^2+6 x-15=0 and x^2+y^2-8 y-10=0 is

Options

  1. A2 (x^2+y^2 )-10 x+5 y=0
  2. B2 (x^2+y^2 )+10 x-5 y=0
  3. C2 (x^2-y^2 )+10 x+5 y=0
  4. D2 (x^2-y^2 )-10 x-5 y=0

Correct answer

A. 2 (x^2+y^2 )-10 x+5 y=0

Step-by-step solution

Let the equation of the circle passing through (0,0) is x^2+y^2+2 g x+2 f y=0 ...(i) and the given equations are x^2+y^2+6 x-15=0 ...(ii) x^2+y^2-8 y-10=0 ...(iii) Eqs. (i) and (ii) are orthogonal. aligned 2 g 3+2 f 0 & =0+(-15) & [ 2 g₁ g₂+2 f₁ f₂=c₁+c₂ ] aligned g=- 5 2 Again Eqs. (i) and (iii) are orthogonal 2 g 0+2 f (-4)=0+(-10) f=5 / 4 The equation of the circle will be x^2+y^2+2 (- 5 2 ) x+2 ( 5 4 ) y=0 2 (x^2+y^2 )-10 x+5 y=0

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