Question

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

• A. ${\tan }^{−1}9$
• B. $\frac{Ï€}{2}−{\tan }^{−1}9$
• C. $\frac{Ï€}{2}+{\tan }^{−1}9$
• D. $\frac{Ï€}{2}$

Answer 1

Answer: (B)

$y=x^2+4x+4−4−17$
$y=(x+2{)}^2−21$
$⇒$ Vertex is $(−2,−21)$
Also $y=x^2+4x−17$
$⇒\frac{dy}{dx}=2x+4$
$⇒$ Slope of tangent at $\left(\frac{5}{2},−\frac{3}{4}\right)$
$m=\frac{dy}{dx}=2×\frac{5}{2}+4=9;θ={\tan }^{−1}9$
$∴$ angle by $y$ -axis $=\frac{π}{2}−{\tan }^{−1}9={\cot }^{−1}9$