Question

The angle of intersection at the origin to the curves $y^2=4x$ and $x^2=4y$ is :

• A. $\pi$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

Given $y^2=4x$

Differentiating w.r.t. $x$, we get,

$2y\frac{dy}{dx}=4$

$\frac{dy}{dx}=\frac{2}{y}.......1$

$x^2=4y$

Differentiating w.r.t. $x$, we get,

$2x=4\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{x}{2}...........2$

So the slope of tangent at $(0,0)$ of $\left(1\right)$ is Parallel to $y$ axis

And the slope of tangent at $(0,0)$ of $\left(2\right)$ is Parallel to $x$ axis

So the angle between them is $\frac{\pi }{2}$