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  4. The equation of a parabola which passes through the intersection of a straight line x + y = 0 and the circle x2 + y 2 + 4y = 0 is :

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Q. 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 :

BITSATBITSAT 2005

Solution:

$x +y=0$
$x^{2}+y^{2}+4 y=0$
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.