Question

The locus of the point of intersection of two tangents to the parabola $y^2=4ax$ which make an angle $\alpha$ with one another is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$tan\alpha \left|\frac{\sqrt{y_1^2-\frac{4a{x}_1}{x_1}}}{1+\frac{a}{x_1}}\right|=\frac{\sqrt{y_1^2-4a{x}_1}}{x_1+a}\Rightarrow (x_1+a{)}^{2}ta{n}^2\alpha =y_1^2-4a{x}_1$
Locus of P is $(x+a{)}^{2}ta{n}^2\alpha =y^2-4ax$