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

Answer: (D)

Given that $y+3x=0$ is the equation of a chord of the circle then
$y=-3x$....(i)
$\left(x^2\right)+{\left(-3x\right)}^2-30x=0$
$10x^2-30x=0$
$10x\left(x-3\right)=0$
$x=0,y=0$
so the equation of the circle is
$\left(x—3\right)\left(x-0\right)+\left(y+9\right)\left(y-0\right)=0$
$x^2-3x+y^2+9y=0$
$x^2+y^2-3x+9y=0$