Question

I: The angle between the curves $y=x^3,6y=7-x^2$ at (1, 1) is $\frac{\pi }{2}$
II:The angle between the curves $y=x,y=\frac{1}{x}$ at (1, 1) is $\frac{\pi }{2}$
Which of the above statements is correct?

• A. I only
• B. II only
• C. both I and II
• D. neither I nor II

Answer 1

The correct option is C both I and II

$\frac{dy}{dx}{|}_{x=11}=3x^2$

$\frac{dy}{dx}=3=m_1$

$6\frac{dy}{dx}=-2x$

$\frac{dy}{dx}=-\frac{1}{3}=m_2$

$m_1\times m_2=-1$

$\therefore$ both curves inclined at 90${}^{\circ }$

$\frac{dy}{dx}=1=m_3$

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

$\frac{dy}{dx}{|}_{x=1}=-1=m_4$

$m_3\times m_4=-1$

$\therefore curvesy=xandy=\frac{1}{x}areat\pi {/}_2$