Question

The angle of intersection of the curve $x^2=4y$ and $y^2=4x$ at point (0,0) is

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

In $x^2=4y$,

$\frac{dy}{dx}=\frac{x}{2}=0at(0,0)\Rightarrow \theta =0$



$y^2=4x\Rightarrow \frac{dy}{dx}=\frac{4}{2\sqrt{4x}}=\infty at(0,0)\Rightarrow \theta =\frac{\pi }{2}$

$\therefore \angle betweenthem={90}^{\circ }$