# Geo4.132

From Example Problems

Tangents are drawn parallel to the line to touch the circles of the coaxal system .Show that the locus of their points of contact is the curve

Given coaxal system

Let P(x_1,y_1) be the point of contact. The equation of the tangent at(x1,y1) to the circle is

. equation be 2.

. this equation be 3.

P lies on the given equation

Slope of 2 is

Given that 2 is parallel to

Hence

Substituting the value of lambda in 3,we get

Therefore, locus of P is