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AP EAMCET202120 Aug 2021Morning ShiftMathematicsCircleActual

The length of the common chord of the circles x 2 + y 2 + 3 x + 5 y + 4 = 0 and x 2 + y 2 + 5 x + 3 y + 4 = 0 is

Options

  1. A3
  2. B2
  3. C6
  4. D4

Correct answer

D. 4

Step-by-step solution

S ≡ x 2 + y 2 + 3 x + 5 y + 4 = 0 and S ' ≡ x 2 + y 2 + 5 x + 3 y + 4 = 0 Equation of common chord is S - S ' = 0 ⇒ - 2 x + 2 y = 0 ⇒ x - y = 0 Centre of S = 0 is C - 3 2 , - 5 2 Radius, r = 9 4 + 25 4 - 4 = 9 2 p = length of the perpendicular from C on A B = - 3 2 + 5 2 1 + 1 = 1 2 A B = length of common chord = 2 r 2 - p 2 = 2 9 2 - 1 2 = 2 4 = 4

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