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

If $P$ and the origin are the points of intersection of the parabolas $y^2=32x$ and $2x^2=27y$,and if $\theta$ is the acute angle between these curves at $P$,then $5\sqrt{\tan \theta} =$

The number of common tangents to the parabolas $y = x^{2}$ and $y = -x^{2} + 4x - 4$ is:

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of its latus rectum. (in $\text{ unit}^{2}$)

The point of intersection of tangents at the ends of the latus rectum of the parabola $y^2 = 4x$ is

$A$ point $P(x, y)$ moves such that its distance from the point $(a, 0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is: