Thank you for reporting, we will resolve it shortly
Q.
The length of the chord of the parabola $y^{2}=4 \text{ax}(a>0)$ which passes through the vertex and makes an acute angle $\alpha$ with the axis of the parabola is
Equation of OP:-
$y=x \tan \alpha$
Solving with $y^{2}=4 a x$, we get :
$x^{2} \tan ^{2} \alpha=4 a x \Rightarrow x=4 a \cot ^{2} \alpha$
Substituting, $y=4 a \cot \alpha$
$\therefore P=\left(4 a \cot ^{2} \alpha, 4 a \cot \alpha\right)$
So, $\overline{O P}=\sqrt{16 a^{2} \cot ^{4} \alpha+16 a^{2} \cot ^{2} \alpha}=4 a \cot \alpha \text{cosec} \alpha$
$\left(\right.$ as $0^{\circ}<\alpha<90^{\circ}$, so, $\cot a>0, \text{cosec} \alpha>0)$
