Question:
The equation of a tangent to the parabola, $\mathrm{x}^{2}=8 \mathrm{y}$, which makes an angle $\theta$ with the positive direction of $\mathrm{x}$-axis, is :
Correct Option: 1
Solution:
$x^{2}=8 y$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{x}}{4}=\tan \theta$
$\therefore \quad \mathrm{x}_{1}=4 \tan \theta$
$\mathrm{y}_{1}=2 \tan ^{2} \theta$
Equation of tangent :-
$y-2 \tan ^{2} \theta=\tan \theta(x-4 \tan \theta)$
$\Rightarrow x=y \cot \theta+2 \tan \theta$