Question

The curves $x^2-y^2=5$ and $\frac{x^2}{18}+\frac{y^2}{8}=1$ cut each other at the common point at an angle

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

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

$x^2=5+y^2$
$\frac{5+y^2}{18}+\frac{y^2}{8}=1$
$40+8y^2+18y^2=144$
$26y^2=104$
$y^2=4$
$y={+}_{-}2$
$x={+}_{-}3$
$y^{\prime }=\frac{x}{y}$
$=\frac{3}{2}=m_1$
$y^{\prime }=-\frac{x\times 8}{18y}$
$=\frac{-3\times 8}{18\times 2}$
$=-3{/}_2=m_2$
$m_1{m}_2=-1$
$\therefore$ Angle between the curves is $\frac{\pi }{2}$