Question

Please answer..i will follow you..
The tangents drawn from the origin to the circle x^2+y^2-2px-2qy+q^2=0 are perpendicular if...

Answer 1

Equation of the given circle can be written as (x-p)^2+(y-q)^2=p^2,

,so that the center of the circle is (p,q) and its radius is p.

This shows that x=0 is a tangent to the circle from the origin .

Since tangent from the origin are perpendicular, equation of the other tangent must be y=0,

which is possible if q=+-p or p^2=q^2.