If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B , then the locus of the foot of perpendicular from O on A B is :

Step-by-step solution

Since, circle passing through origin intersect the coordinate axes at A &   B , hence A B must be diameter and A B = 2 R . Now, let foot of the perpendicular from origin upon A B be P h ,   k . Slope of line O P = k - 0 h - 0 = k h Since, line A B ⊥ O P ⇒ slope of A B = - h k Thus, equation of line A B is y - k = - h k x - h For co-ordinates of A , put y = 0 ⇒ 0 - k = - h k x - h ⇒ x = h 2 + k 2 h ⇒ A   h 2 + k 2 h ,   0 . For co-ordinates of B , put x = 0 &#865