If two perpendicular tangents are drawn from a point $P$ to the parabola $y^2 = 4x$,find the locus of $P$.

The line $y=mx+1$ is a tangent to the curve $y^{2}=4x$ if the value of $m$ is

The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola $y^2 = 4ax$ lies on

$A$ set of parallel chords of the parabola $y^2 = 4ax$ have their mid-points on:

Let $P(\alpha, \beta)$ be a point on the parabola $y^2 = 4x$. If $P$ also lies on the chord of the parabola $x^2 = 8y$ whose midpoint is $(1, 5/4)$,then $(\alpha - 28)(\beta - 8)$ is equal to:

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are