Question

Let S ≡ x² + y² + 2gx + 2fy + c = 0 be a given circle. Find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

Answer 1

Let, P(h,k) be the foot of perpendicular drawn from origin O(0, 0) on the chord AB of the given circle such that the chord AB subtends a right angle at the origin.

The combined equation of OA and OB is homogeneous equation of second degree obtained by the help of the given circle and the chord AB and is given by,