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 :

Question

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 : (A) y2 =4x (B) y2 =x (C) y2 =2x (D) none of these

Tardigrade Admin · Accepted Answer

x +y=0 x2+y2+4 y=0 The line and the circle intersect at the point (0,0) and (2,-2) Among the given options, only y2=2 x passes through both these points.

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

$y^{2} = 4 x$

$y^{2} = x$

$y^{2} = 2 x$

none of these

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

Q. 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 :

y2=4x

y2=x

y2=2x