Question

If $\theta$ denotes the angle between the curves $y=30-2x^2$ and $y=3+x^2$ at a point of their intersection, then $71|\tan \theta |$ is equal to

• A. $15$
• B. $13$
• C. $20$
• D. $18$

Answer 1

The correct option is D $18$

$y=30-2x^2\Rightarrow m_1=-4x$
$y=3+x^2\Rightarrow m_2=2x$
$\tan \theta =|\frac{m_1-m_2}{1+m_1{m}_2}|=|\frac{-4x-2x}{1-8x^2}|=|\frac{-6x}{1-8x^2}|$
For point of intersection, $30-2x^2=3+x^2$
$\Rightarrow 3x^2=27\Rightarrow x^2=9\Rightarrow x=\pm 3$
$\Rightarrow |\tan \theta |=|\frac{-18}{1-8\times 9}|=|\frac{-18}{-71}|=\frac{18}{71}$
$\Rightarrow 71|\tan \theta |=18$