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Q.
The polars of $(-1,2)$ with respect to the two circles $S _1 \equiv x^2+y^2+6 y+7=0$ and $S _2 \equiv x^2+y^2+6 x+1=0$
TS EAMCET 2021
Solution:
$ S_1 \Rightarrow x^2+y^2+6 y+7=0 $
$ S_2 \Rightarrow x^2+y^2+6 x+1=0$
Equation of polar of $(-1,2)$ on $S_1$ is
$-x+2 y+3(y+2)+7=0 $
$ \Rightarrow -x+5 y+13=0 \ldots \text { (i) }$
Equation of polar on $S_2$ is
$\Rightarrow-x+2 y+3(x-1)+1=0$
$x+y-1=0$
From Eqs. (i) and (ii)
$x=3 \text { and } y=-2$