Question

The angle of intersection of the curve $y=x^2$ and $6y=7-x^3$ at $(1,1)$ is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. None of these

Answer 1

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

$y=x^2\Rightarrow \frac{dy}{dx}=2x\Rightarrow m_1=2$ at

$(1,1)$

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

$\Rightarrow \frac{dy}{dx}=-\frac{1}{2}$ at $(1,1)$

$\Rightarrow m_2=-\frac{1}{2}$

$\therefore m_1{m}_2=-1$ at $(1,1)$

$\Rightarrow \theta =\frac{\pi }{2}$