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AP EAMCET · Maths · Circle

If \(2 \mathrm{x}-3 \mathrm{y}+1=0\) is the equation of the polar of a point \(\mathrm{P}\left(\mathrm{x}_1, \mathrm{y}_1\right)\) with respect to the circle \(x^2+y^2-2 x+4 y+3=0\), then \(3 x_1-y_1=\)

  1. A \(\frac{1}{3}\)
  2. B \(-3\)
  3. C \(3\)
  4. D \(-\frac{1}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(3\)

Step-by-step Solution

Detailed explanation

\(x^2+y^2-2 x+4 y+3=0 \implies g=-1, f=2, c=3\) Polar of \(P(x_1, y_1)\) is \(x x_1 + y y_1 + g(x+x_1) + f(y+y_1) + c = 0\) \(x x_1 + y y_1 - (x+x_1) + 2(y+y_1) + 3 = 0\) \(x(x_1-1) + y(y_1+2) + (-x_1+2y_1+3) = 0\) Comparing with \(2x - 3y + 1 = 0\):…