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. $\left(2,2\right)$
• B. $\left(4,-4\right)$
• C. $\left(4,4\right)$
• D. $\left(-2,2\right)$

Answer 1

The correct option is C

$\left(4,4\right)$

Explanation for correct option

Given two parabolas are

$x^2=4y$ …………(i)

$y^2=4x$ ……….(ii)

From equation (ii) we get

$$\begin{gathered} y^2=4x \\ \Rightarrow y^4={\left(4x\right)}^2 \\ \Rightarrow y^4=16x^2 \end{gathered}$$

Now using equation (i) we get

$$\begin{gathered} \Rightarrow y^4=16\left(4y\right) \\ \Rightarrow y^4-64y=0 \\ \Rightarrow y\left(y^3-4^3\right)=0 \\ \Rightarrow y=0,4 \end{gathered}$$

Putting the value of $y$ in equation (i) we get

$x=0,4$

Therefore the intersection of the points are $(0,0),(4,4)$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{C}\right)$