Question

The polar of $(1,-2)$ with respect to $x^{2}+y^{2}-10 x-10 y+25=0$ is

• A. $4 x+7 y+30=0$
• B. $4 x+7 y-30=0$
• C. $4 x-7 y+30=0$
• D. $x+y=0$

Answer 1

Answer: (B)

Given circle is,
$x^{2}+y^{2}-10 x-10 y+25=0$
Given point ' $P$ is $(1,-2)$
Equation of polar of point $P$ with respect to circle is,
$x \cdot 1+y(-2)-10\left(\frac{x+1}{2}\right)-10\left(\frac{y-2}{2}\right)+25=0$
$\Rightarrow x-2 y-5(x+1)-5(y-2)+25=0$
$\Rightarrow x-2 y-5 x-5-5 y+10+25=0$
$\Rightarrow -4 x-7 y+30=0$
$\Rightarrow 4 x+7 y-30=0$