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VITEEE 2021 Paper

Section: Mathematics

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Question : 64 of 80

Marks: +1, -0

The angle of intersection to the curve

y=x^{2}

6 y=7-x^{3}

(1,1)

is :

$\frac{\pi}{2}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$
π

Solution:

Let

m_{1}

and

m_{2}

be slope of curve

y=x^{2}

and

6 y=7-x^{3}

respectively.

Now,

y=x^{2} \Rightarrow \frac{d y}{d x}=2 x

⇒

\left(\frac{dy}{dx}\right)_{(1,1)}=2

i.e.

m_{1}=2

and

6 y=7-x^{3} \Rightarrow 6 \frac{dy}{dx}=-3 x^{2}

⇒

\frac{dy}{dx}=-\frac{3}{6} x^{2}=-\frac{1}{2} x^{2}

⇒

\left(\frac{dy}{dx}\right)_{(1,1)}=-\frac{1}{2}(1)^{2}=-\frac{1}{2}

∴

m_{2}=-\frac{1}{2}

\therefore m_{1} m_{2}=2 -\frac{1}{2}=-1

∴ Angle of intersection is

90^{\circ}

i.e.

\frac{\pi}{2}

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