Question

Two parabolas $x^2=4y$ and $y^2=4x$ intersect at two distinct points out of which one of them is origin then the other point will be

• A. $(2,2)$
• B. $(4,-4)$
• C. $(4,4)$
• D. $(-2,2)$

Answer 1

The correct option is C $(4,4)$

$x^2=4y$ $\cdots \cdots \left(1\right)$
$y^2=4x$ $\cdots \cdots \left(2\right)$
Solving equations $\left(1\right)$ and $\left(2\right)$, we get
$x^2=4\times 2\sqrt{x}$
or
$x^2=4\times (-2)\sqrt{x}$ (not possible)
$\therefore x^2=4\times 2\sqrt{x}$
$\Rightarrow (x{)}^{\frac{3}{2}}=(4{)}^{\frac{3}{2}}$
$\Rightarrow x=4$
$\therefore y=4$
Hence, other point is $(4,4)$