If the bisector of angle `A P B ,` where `P Aa n dP B` are the tangents to the parabola `y^2=4a x ,` is equally, inclined to the coordinate axes, then the point `P` lies on the tangent at vertex of the parabola directrix of the parabola circle with center at the origin and radius `a` the line of the latus rectum.

Options

A. tangent at vertex of the parabola
B. directrix of the parabola
C. circle with center at the origin and radius
D. the line of latus rectum

Answer

D

Explanation

(4)
Here, `(1)/(t_(1))="tan"((pi)/(4)+theta)`
`and(1)/(t_(2))="tan"((pi)/(4)-theta)`
So, `t_(1)t_(2)=1`
Therefore, the x-coordinate of P is `at_(1)t_(2),i.e.,a`.