Two perpendicular tangents to the circle  x2+y2 =a2 meet at P. Then the locus of P has the equation

Let the coordinates of P be  (h, k). Then, the equation of the tangents drawn from P(h,k)  to  x2+y2=a2 is x2+y2−a2h2+k2−a2=hx+ky−a22                  [Using SS' =T2 ]This equation represents a pair of perpendicular lines.  Coeff. of x2+ Coeff. of y2=0 ⇒h2+k2−a2−h2+h2+k2−a2−k2=0 ⇒h2+k2=2a2 Hence, the locus of  (h,k) is x2+y2=2a2.