Question

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. $(-2,2)$

Answer 1

Answer: (C)

$(4,4)$

Given, equations of parabola are $x^2=4y$ and $y^2=4x$ ... $\left(i\right)$
$\therefore {\left(\frac{x^2}{4}\right)}^2=4x$
$\Rightarrow x^4-64x=0$
$\Rightarrow x=0,x=4$
On putting the values of $x$ in Eq. $\left(i\right),$ we get $y=0$ and $y=4,-4$

$(\because y=-4$ does not satisfy the eqation $x^2=4y)$
Thus, the points of intersection are $(0,0)$ and $(4,4)$.

Hence, the point other than origin is $(4,4)$.