For the parabola $y^{2} = 4x$,the point $P$ whose focal distance is $17$ is

If $P$ is a point on the parabola $y^{2}=4ax$ with focus $F$. Let $Q$ denote the foot of the perpendicular from $P$ onto the directrix. Then, $\frac{\tan \angle PQF}{\tan \angle PFQ}$ is

The latus rectum of a parabola whose focal chord $PSQ$ is such that $SP = 3$ and $SQ = 2$ is given by

The ordinates of the points $P$ and $Q$ on the parabola with focus $(3,0)$ and directrix $x = -3$ are in the ratio $3:1$. If $R(\alpha, \beta)$ is the point of intersection of the tangents to the parabola at $P$ and $Q$,then $\frac{\beta^2}{\alpha}$ is equal to $.............$.

Let the tangent and normal at any point $P(at^2, 2at)$, $(a > 0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is

The equation of the normal to the parabola $y^2 = 4ax$ at the point $\left( \frac{a}{m^2}, \frac{2a}{m} \right)$ is: