The angle formed by the abscissa and the tangent to the parabola $y=x^2+4 x-17$ at the point $\frac{5}{2},-\frac{3}{4}$ is
Answer & explanation
Correct answer: option 4
Slope of x-axis is 0.
$y=x^2+4 x-17 \Rightarrow \frac{d y}{d x}=2 x+4$
∴ slope of tangent to parabola at $P\left(\frac{5}{2},-\frac{3}{4}\right)$
$=2\left(\frac{5}{2}\right)+4=9$
If $\theta$ is the angle between x-axis and the tangent at P then $\tan \theta=9 \Rightarrow \tan ^{-1} 9$.