Find the polar of the point $\left(3, 4\right)$ with respect to the circle $x^2 + y^2 = 25$.
Given point: $\;\;$ $\left(h, k\right) = \left(3, 4\right)$
Given circle: $\;\;$ $x^2 + y^2 = 25$
Comparing the equation of the given circle with the standard equation of circle $\;\;$ $x^2 + y^2 = r^2$
gives $\;\;$ $r^2 = 25$
The polar of $\;$ $\left(h, k\right)$ $\;$ with respect to the circle $\;$ $x^2 + y^2 = r^2$ $\;$ is $\;$ $xh + yk = r^2$
$\therefore \;$ The required polar is: $\;$ $3x + 4y = 25$