Question

Angle formed by the positive Y-axis and the tangent to $y=x^{2}+4 x-17$ at $\left(\frac{5}{2}, \frac{-3}{4}\right)$ is

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

Answer 1

Answer: (B)

$y=x^{2}+4 x+4-4-17$
$y=(x+2)^{2}-21$
$ \Rightarrow $ Vertex is $(-2,-21)$
Also $y=x^{2}+4 x-17 $
$\Rightarrow \frac{d y}{d x}=2 x+4$
$\Rightarrow $ Slope of tangent at $\left(\frac{5}{2},-\frac{3}{4}\right)$
$m=\frac{d y}{d x}=2 \times \frac{5}{2}+4=9 ; \theta=\tan ^{-1} 9$
$\therefore $ angle by $y$ -axis $=\frac{\pi}{2}-\tan ^{-1} 9=\cot ^{-1} 9$