Question

The angle formed by the positive $y-axis$ and the tangent to $y=x^2+4x-17$ at $(5/2,-3/4)$ is

• 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. none of these

Answer 1

Answer: (B), (C)

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

Slope of tangent to given curve at $\frac{5}{2},-\frac{3}{4}$ is 9.

If $\theta$ is the angle between the tangent and x-axis , then $\theta =\pm ta{n}^{-1}9$

Angle between y-axis and x-axis is $\frac{\pi }{2}$

So, the angle between y-axis and tangent is $\frac{\pi }{2}\pm ta{n}^{-1}9$