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AP EAMCET20224 Jul 2022Morning ShiftMathematicsCircleActual

The pole of the line x a + y b = 1 with respect of the circle x 2 + y 2 = c 2 is

Options

  1. Ac 2 a , c 2 b
  2. Bc 2 b , c 2 a
  3. Cc a , c b
  4. Dc b , c a

Correct answer

A. c 2 a , c 2 b

Step-by-step solution

Let P x 1 , y 1 be a pole with respect to the circle x 2 + y 2 = c 2 Then polar equation is given by, T = 0 ⇒ x x 1 + y y 1 - c 2 = 0 → 1 ⇒ x x 1 c 2 + y y 1 c 2 - 1 = 0 Since P x 1 , y 1 lies on x a + y b = 1 ⇒ x 1 a + y 1 b - 1 = 0 → 2 Now comparing with equation 1 and equation 2 we get point x 1 , y 1 ≡ c 2 a , c 2 b

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