If the inverse of P(-3, 5) with respect to a | vedclass

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(C) Let the circle be $S = x^2 + y^2 + 2gx + 2fy + c = 0$. Given that the inverse of $P(-3, 5)$ is $A(1, 3)$. The polar of $P$ is a line perpendicular

Vedclass · Accepted Answer

$2x - y + 1 = 0$

Vedclass · Answer

(C) Let the circle be $S = x^2 + y^2 + 2gx + 2fy + c = 0$. Given that the inverse of $P(-3, 5)$ is $A(1, 3)$. The polar of $P$ is a line perpendicular to the line joining the center of the circle to $P$. However,a fundamental property of the polar is that it passes through the inverse point $A(1, 3)$ and is perpendicular to the line $OP$ (where $O$ is the center). Since the polar is perpendicular to the line $PA$,the slope of $PA$ is $m_{PA} = \frac{3 - 5}{1 - (-3)} = \frac{-2}{4} = -\frac{1}{2}$. The slope of the polar line is $m = -\frac{1}{m_{PA}} = 2$. The polar passes through $A(1, 3)$,so its equation is $y - 3 = 2(x - 1)$. $y - 3 = 2x - 2$. $2x - y + 1 = 0$.

If the inverse of $P(-3, 5)$ with respect to a circle is $(1, 3)$,then the polar of $P$ with respect to that circle is

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