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 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
$\left(x?3\right) \left(x-0\right) + \left(y+ 9\right) \left(y-0\right) = 0$
$x^{2}-3x + y^{2} + 9y=0$
$x^{2} + y^{2}-3x + 9y=0$