Question

The angle(s) formed by the positive $y-$axis and the tangent to $y=x^2+4x-17$ at $(\frac{5}{2},\frac{-3}{4})$ is(are)

• A. ${\tan }^{-1}\left(9\right)$
• B. $\frac{\pi }{2}-{\tan }^{-1}\left(9\right)$
• C. $\frac{\pi }{2}+{\tan }^{-1}\left(9\right)$
• D. $\pi -{\tan }^{-1}\left(9\right)$

Answer 1

Answer: (B), (C)

$\frac{\pi }{2}+{\tan }^{-1}\left(9\right)$

$\frac{dy}{dx}=2(x+2)$
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\frac{5}{2}}=9$
$\Rightarrow \tan \theta =9$
Angle with $y-$ axis $=\frac{\pi }{2}\pm \theta$
$=\frac{\pi }{2}\pm {\tan }^{-1}\left(9\right)$