Question

The equation of a parabola which passes through the intersection of a straight line $x + y = 0$ and the circle $x^2 + y ^2 + 4y = 0$ is :

• A. $y^2 =4x$
• B. $y^2 =x$
• C. $y^2 =2x$
• D. none of these

Answer 1

Answer: (C)

$y^2 =2x$

Answer 2

$x +y=0$
$x^{2}+y^{2}+4 y=0$
The line and the circle intersect at the point $(0,0)$ and $(2,-2)$
Among the given options, only $y^{2}=2 x$ passes through both these points.