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
A) $y^{2} = 4x$
B) $y^{2} = x$
C) $y^{2} = 2x$
D) None of these
Explanation
(c)
The interesetion of line and circle is (0, 0) and (2, -2). Now, taking option (c),
$ie\ \ y^{2} = 2x$
At point (0,0) $\Rightarrow 0 = 0$
and at point $(2, - 2) \Rightarrow ( - 2)^{2} = 2(2)\ \Rightarrow \ 4 = 4$
Hence, option (c) is the correct answer
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.