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

y^{2} = 4 x

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y^{2} = x

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y^{2} = 2 x

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None of these

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Solution

The correct option is C $y^{2} = 2 x$
$x + y = 0$
$x^{2} + y^{2} + 4 y = 0$
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.

So, the answer is option (C).

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The equation of a parabola which passes through the intersection of a straight line x+y=0 and the circle x2+y2+4y=0 is.

The correct option is C y2=2xx+y=0x2+y2+4y=0The line and the circle intersect at the point (0,0) and (2,−2)Among the given options, only y2=2x passes through both these points.So, the answer is option (C).

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

The correct option is C $y^{2} = 2 x$
$x + y = 0$
$x^{2} + y^{2} + 4 y = 0$
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.

So, the answer is option (C).