Mathematics - Parabola Question with Solution | TestHub

Let $A$ vertex, $\mathrm{AP}=$ chord of $x^2=4y$ such that slope of AP is $\cot \alpha$

Let $P=(2t,t^2)$ Slope of $AP=\frac{1}{2}\Rightarrow \cot \alpha =\frac{1}{2}\Rightarrow t=2\cot \alpha$

Now, $AP=\sqrt{4t^2+t^4}=t\sqrt{4+t^2}$

$$\begin{array}{rl}& =4\cot \alpha \mathrm{cosec}\alpha \\ & =4\cos \alpha \cdot {\mathrm{cosec}}^2\alpha \end{array}$$