# Geo4.38

From Example Problems

Find the locus of point of intersection of two perpendicular tangents to the circle

Given circle is

Let this equation be 1.

Let (x1,y1) be the point of intersection of two pependicular tangents.

Equation of a tangent to equation 1 is

Let this equation be 2.

The equation 2 passes thro' (x1,y1), we have

Simplifying

Rearranging

If m1,m2 are the two slopes of two tangents from (x1,y1) to 1,m1,m2 are the roots of the above quadratic equation,

Given two tangents are pependicular to each other, m1m2=-1

Hence

Now the locus of the point (x1,y1) is