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AP EAMCET202120 Aug 2021Evening ShiftMathematicsCircleActual

The equation of radical axis of the circles x 2 + y 2 + 4 x + 6 y + 7 = 0 and 4 x 2 + 4 y 2 + 8 x + 12 y - 9 = 0 is

Options

  1. Ax + y + 1 = 0
  2. B8   x + 12   y = 0
  3. C8   x + 12   y + 37 = 0
  4. D2   x + 3   y + 7 = 0

Correct answer

C. 8   x + 12   y + 37 = 0

Step-by-step solution

Given: S 1 :   x 2 + y 2 + 4 x + 6 y + 7 = 0 S 2 :   4 x 2 + 4 y 2 + 8 x + 12 y - 9 = 0 Equation of radical axis of circles is S 1 - S 2 = 0 S 1 :   x 2 + y 2 + 4 x + 6 y + 7 = 0 S 2 :   x 2 + y 2 + 2 x + 3 y - 9 4 = 0 Radical axis: S 1 - S 2 = 0 ⇒   x 2 + y 2 + 4 x + 6 y + 7 - x 2 + y 2 + 2 x + 3 y - 9 4 = 0 ⇒   2 x + 3 y + 37 4 = 0 ⇒   8 x + 12 y + 37 = 0

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