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AP EAMCET · Maths · Circle

If the equation of the polar of the point \((\alpha,-1)\) with respect to the circle \(x^2+y^2-4 x-6 y-12=0\) is \(y=\beta\), then \(4(\alpha+\beta)=\)

  1. A \(-5\)
  2. B \(7\)
  3. C \(-6\)
  4. D \(0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(-5\)

Step-by-step Solution

Detailed explanation

Polar of \((\alpha, -1)\) w.r.t. \(x^2+y^2-4x-6y-12=0\): \(x(\alpha) + y(-1) - 2(x+\alpha) - 3(y-1) - 12 = 0\) \(\alpha x - y - 2x - 2\alpha - 3y + 3 - 12 = 0\) \((\alpha-2)x - 4y - 2\alpha - 9 = 0\) Given polar is \(y=\beta\), so coefficient of \(x\) must be \(0\).…