If y + 3 x = 0 is the equation of a chord of the circle x 2 + y 2 - 30 x = 0 , then the equation of the circle with this chord as diameter is :

Step-by-step solution

To find point of intersection of given chord y = - 3 x with the given circle x 2 + y 2 - 30 x = 0 eliminate y from two equations Point of intersection ⇒ x 2 + 9 x 2 - 30 x = 0 ⇒ 10 x   x - 3 = 0 ⇒ x = 0 or x = 3 Therefore, y   =   0 and y   = - 9 are the corresponding ordinates. Point of intersection ( 0 ,   0 ) , ( 3 ,   - 9 ) Diametric form of equation of circle, x   x - 3 + y y + 9 = 0 ⇒ x 2 + y 2 - 3 x + 9 y = 0 .