If $x-y-3=0$ is a normal drawn through the point $(5,2)$ to the parabola $y^2=4x$,then the slope of the other normal that can be drawn through the same point to the parabola $y^2=4x$ is

What is the angle subtended by the latus rectum of the parabola $y^2 = ax$ at its vertex?

The angle of intersection between the curves $x^2 = 4(y + 1)$ and $x^2 = -4(y + 1)$ is

The straight line $y = 2x + \lambda$ does not meet the parabola $y^2 = 2x$,if

Suppose $AB$ is a focal chord of the parabola $y^2=12x$ of length $l$ and slope $m < \sqrt{3}$. If the distance of the chord $AB$ from the origin is $d$,then $l \cdot d^2$ is equal to ....................

The equation of the directrix for the parabola $4x^{2}-4x-2y+3=0$ is