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…

To find point of intersection of given chord $y=-3x$ with the given circle $x^2+y^2-30x=0$ eliminate $y$ from two equations
Point of intersection  
$\Rightarrow$ $x^2+9x^2-30x=0$
$\Rightarrow$ $10x \left(x-3\right)=0$
$\Rightarrow$ $x=0$ 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,
$x \left(x-3\right)+y\left(y+9\right)=0$
$\Rightarrow x^2+y^2-3x+9y=0$ .