The locus of the mid points of a chord of the circle $x^2+y^2=4$ which subtends a right angle at the origin, is

detailed solution

Correct option is C

Let (h, k) be the coordinates of the mid point of a chord which subtends a right angle at the origin. Then equation of the chord is hx+ky−4=h2+h2−4                                        [Usin⁡gT=S]⇒hx+ky=h2+k2The combined equation of the pair of lines joining the origin to the points of intersection of x2+y2=4 and hx+ky=h2+k2x2+y2−4hx+kyh2+k22=0Lines given by the above equation are at right angle. Therefore.  Coeff. of x2+ Coeff. of y2=0⇒ 2h2+k22−4h2+4k2=0⇒ h2+k2=2Hence, the locus of (h,k) is x2+y2=2