If y=2x is a chord of the circle x2+y2=10x, then the equation of  the circle whose diameter is this  chord, is -

Equation of circle passing through the points of intersection of the given circle and the chord is x2+y2−10x+k2x−y=0x2+y2+x−10+2k−ky=0center5−k,k2it lies on the line y=2xk2=10−2kk=20−4kk=4Therefore, the equation of the circle is x2+y2+x−10+8−4y=0x2+y2−2x−4y=0