Question

Find the value of k, if the point (1, 3) and (2, k) are conjugate with respect to the circle $x^2+y^2=35$.

Answer 1

Since points $(1,3)$ and $(2,k)$ are conjugate w.r.t. the given circle, both the points lie on the polar of the other point.

$\therefore (1,3)$ lies on $x\left(2\right)+y\left(k\right)-35=0$

i.e. $2\times 1+3\times k-35=0$

$\therefore 3k=33$ or $k=11$