Question

The pole of the straight line $x+2y=1$ with respect to the circle $x^2+y^2=5$, is.

• A. $(5,6)$
• B. $(5,10)$
• C. $(10,5)$
• D. $(10,10)$

Answer 1

The correct option is B $(5,10)$

Let the pole be $\left(x_1{y}_2\right)$, then the equation of the polar with respect to the circle $x^2+y^2=5$ is $x{x}_1+y{y}_1=5$ .....$\left(i\right)$
Eq. $\left(i\right)$ and $x+2y=1$ represents the same staright line.
$\Rightarrow x_1=5,y_1=10$
$\therefore$ Pole is $(5,10)$.