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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

The equation of the circle, which cuts orthogonally each of the three circles x 2 + y 2 - 2 x + 3 y - 7 = 0 , x 2 + y 2 + 5 x - 5 y + 9 = 0 and x 2 + y 2 + 7 x - 9 y + 29 = 0

Options

  1. Ax 2 + y 2 − 16 x − 18 y − 4 = 0
  2. Bx 2 + y 2 = 16
  3. Cx 2 + y 2 − 16 x = 0
  4. Dy 2 − x 2 + 2 x = 0

Correct answer

A. x 2 + y 2 − 16 x − 18 y − 4 = 0

Step-by-step solution

Assuming, we have a circle x 2 + y 2 + 2 g x + 2 f y + c = 0     . . . 1 which cuts circles x 2 + y 2 - 2 x + 3 y - 7 = 0     . . . 2 , x 2 + y 2 + 5 x - 5 y + 9 = 0     . . . 3 and x 2 + y 2 + 7 x - 9 y + 29 = 0     . . . 4 orthogonally, Applying condition for two circles intersecting orthogonally, So, considering equations 1 and 2 , 2 g - 1 + 2 f 3 2 = c - 7 ⇒ - 2 g + 3 f - c = - 7     . . . 4 Similarly, considering equations 1 and 3 2 g 5 2 + 2 f - 5 2 = c

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