If y+3x=0 is the equation of a chord of the circle x^2+y^2-30x=0, then the equation of the…

Question

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

Accepted Answer

Put $y=-3x$ into $x^2+y^2-30x=0$: $10x^2-30x=0\Rightarrow x=0$ or $x=3$, giving points $(0,0)$ and $(3,-9)$.

Circle on these as diameter: $(x-0)(x-3)+(y-0)(y+9)=0\Rightarrow x^2+y^2-3x+9y=0.$

Solutions · 1