# Geo5.2.39

From Example Problems

Prove that the pair of tangents drawn to are perpendicular to eachother.

Given and Let the point be

Therefore,equation to the pair of tangents is

Separating the coefficients of and

From the above,the sum of the coefficients of squares of x and y is zero,which is the condition for the two lines to be perpendicular.

Hence the two tangents drawn on the given ellipse are perpendicular to each other.