Question

The angle between the curves $2x^2+y^2=20$ and $4y^2-x^2=8$ at the point $(2\sqrt{2},2)$

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

Answer 1

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

$y^{\prime }=-\frac{2x}{y}$
$y^{\prime }=-\frac{2\times 2\sqrt{2}}{2}$
$=-2\sqrt{2}=m_1$
$y^{\prime }=\frac{x}{4y}$
$=\frac{2\sqrt{2}}{2\times 4}$
$=\frac{1}{2\sqrt{2}}=m_2$
$m_1{m}_2=-1$
$\therefore$ Angle b/w the curve $\pi /2$