Q. The two parabolas $x^{2} = 4y\$ and $y^{2} = 4x$ meet in two distinct points. One of these is the origin and the other is
A) (2,2)
B) $(4, - 4)$
C) (4,4)
D) $( - 2,2)$
Explanation
(c)
Given equation of parabola are
$x^{2} = 4y\$and$\ y^{2} = 4s$ …(i)
$\therefore\left( \frac{x^{2}}{4} \right)^{2} = 4x\ \Rightarrow \ x^{2} - 64x = 0\$
$\Rightarrow x = 0,\ x = 4\$
On putting the values of $x$ in Eq. (i), we get
$y = 0$ and$\ y = 4$
Hence, points of intersection are (0, 0) and (4, 4)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.