The correct option is C x2+y2=2a2
Equation of a tangent to the circle x2+y2=a2 is y = mx + a√1+m2 → (1)
Equation of a tangent to the circle x2+y2=a2 and perpendicular to (1) is
y = (−1m) x + a √1+(−1m) ⇒ y = - xm + a√1 + m2m ⇒ my = - x + a√1+m2 → (2)
From (1), y - mx = a√1+m2
From (2), my + x = a√1+m2
Squaring and adding the above questions, we get (y−mx)2+(my+x)2=a2(1+m2)+a2(1+m2)
⇒(1+m2)x2+(1+m2)y2=2a2(1+m2)
⇒x2+y2=2a2 which is the required locus.