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AP EAMCET · Maths · Circle

If the pole of the line \(x+2 b y-5=0\) with respect to the circle \(S \equiv x^2+y^2-4 x-6 y+4=0\) lies on the line \(x+b y+1=0\), then the polar of the point \((b,-b)\) with respect to the circle \(S=0\) is

  1. A \(5 y-6=0\)
  2. B \(y-6=0\)
  3. C \(x+5 y-6=0\)
  4. D \(5 x+y-6=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(5 y-6=0\)

Step-by-step Solution

Detailed explanation

The circle \(S\) is \(x^2+y^2-4 x-6 y+4=0\). The polar of a point \((x_1, y_1)\) with respect to \(S=0\) is \(x x_1+y y_1-2(x+x_1)-3(y+y_1)+4=0\). Rearranging, this is \(x(x_1-2)+y(y_1-3)-(2x_1+3y_1-4)=0\). Comparing with the given line \(x+2 b y-5=0\), we have:…