Question

The length of the chord of the parabola $x^2=4y$ passing through the vertex and having slope $cot\alpha$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let A = vertex, AP = chord of $x^2=4y$ such that slope of AP is $cot\alpha$ Let $P=(2t,t^2)SlopeofAP=\frac{t}{2}\Rightarrow cot\alpha =\frac{t}{2}\Rightarrow t=2cot\alpha$ Now,AP$=\sqrt{4t^2+t^4}=t\sqrt{4+t^2}$ $=4cot\alpha cosec\alpha$ $=4cos\alpha .cose{c}^2\alpha$