The tangents drawn from the origin to the circle x2+y2- 2px–2qy+q2=0 are perpendicular if

Equation of the given circle can be written as       (x−p)2+(y−q)2=p2                      (i)This has (p, q) as the centre and p as the radius showing that it touches y-axis. So one of the tangents from the origin to the circle is y-axis.⇒     Other tangent from the origin to the circle must be x-axis. which is possible if q = ± p.⇒   p2−q2=0.