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
- A \(5 y-6=0\)
- B \(y-6=0\)
- C \(x+5 y-6=0\)
- D \(5 x+y-6=0\)
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:…
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