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AP EAMCET202120 Aug 2021Morning ShiftMathematicsCircleActual

Find the equation of the circle which passes through origin and cuts off the intercepts - 2 and 3 over the x and y axes respectively.

Options

  1. Ax 2 + y 2 - 2 x + 8 y = 0
  2. B2 x 2 + y 2 + 2 x - 3 y = 0
  3. Cx 2 + y 2 - 2 x - 8 y = 0
  4. Dx 2 + y 2 + 2 x - 3 y = 0

Correct answer

D. x 2 + y 2 + 2 x - 3 y = 0

Step-by-step solution

Equation of circle = x 2 + y 2 + 2 g x + 2 f y + c = 0 which passes through 0 , 0 , - 2 , 0 , 0 , 3 When it passes through 0 , 0 , then c = 0 When it passes through - 2 , 0 , then 4 - 4 g = 0 ⇒ g = 1 When it passes through 0 , 3 , then 9 + 6 f = 0 ⇒ f = - 3 2 Hence, the required equation of circle is x 2 + y 2 + 2 x - 3 y = 0 .

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