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

• A. $x^2+y^2-3x-9y=0$
• B. $x^2+y^2+3x+9y=0$
• C. $x^2+y^2-3x+9y=0$
• D. $x^2+y^2+3x-9y=0$

Answer 1

The correct option is C $x^2+y^2-3x+9y=0$

$y+3x=0x^2+y^2-30x=0\Rightarrow x^2+(-3x{)}^2-30x=0\Rightarrow 10x(x-3)=0\Rightarrow x=0,3\Rightarrow x=0,y=0x=3,y=-9$
Equation of the circle whose end points of the diameter are $(0,0)$ and $(3,-9)$ is
$(x-3)(x-0)+(y+9)(y-0)=0\Rightarrow x^2+y^2-3x+9y=0$