Question

The angle between the curves $x^2=4y$ and $y^2=4x$ at (4, 4) is

• A. $\frac{\pi }{2}$
• B. $ta{n}^{-1}\left(3\right)$
• C. $ta{n}^{-1}\left(\frac{3}{4}\right)$
• D. $ta{n}^{-1}\left(\frac{4}{3}\right)$

Answer 1

The correct option is C $ta{n}^{-1}\left(\frac{3}{4}\right)$

$\frac{2x}{4}=\frac{dy}{dx}$

$y^{\prime }{|}_{x=4}=2=m_1$

$2y\cdot y^1=4$

$y^{\prime }{|}_{x=4,y=4}=\frac{1}{2}=m_2$

$tan{\theta }^{}=\frac{m_1-m_2}{1+m_1{m}_2}$

${\theta }^{}=ta{n}^{-1}\left(\frac{3}{4}\right)$