# Geo4.45

From Example Problems

Find the equation of the circle with centre on the line 2x+y=0 and which touches the lines 4x-3y+10=0 and 4x-3y-30=0.

Let the required circle be

The centre is(-g,-f) and radius is

The centre lies on

Hence

The distance from the centre to the first line =radius

Squaring on both sides,we get

Now

Similarly for the second line, we have

Substracting these two equations, we have

The equation of the required circle is