Q. The angle of intersection of the curves $y = x^{2},\ 6y = 7 - x^{3}$ at (1, 1) is
A) $\frac{\pi}{4}$
B) $\frac{\pi}{3}$
C) $\frac{\pi}{2}$
D) None of these
Explanation
(c)
Given equation of curves are $y = x^{2}$ and $6y = 7 - x^{3}$
$\therefore\ \ \ \ \ m_{1} = \left( \frac{dy}{dx} \right)_{(1,\ 1)} = 2(1) = 2$
And $m_{2} = \left( \frac{dy}{dx} \right)_{(1,\ 1)} = - \frac{1}{2}$
Now, $m_{1}m_{2} = 2 \times \left( - \frac{1}{2} \right) = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.