Three normals are drawn from the point $(c, 0)$ to the curve $y^2=x$. If one of the normals is the $X$-axis,then the value of $c$ for which the other two normals are perpendicular to each other is

The coordinates of the focus of the parabola $(x+3)^2 = 2(y-5)$ are

If $x = t^2$ and $y = 2t$,then the equation of the normal at $t = 1$ is

If $y=mx+4$ is a tangent to both the parabolas $y^{2}=4x$ and $x^{2}=2by$,then $b$ is equal to:

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?

Let $P$ be a point on the parabola $y^2 = 4ax$,where $a > 0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $PFQ$,where $F$ is the focus of the parabola,is $120$. If the slope $m$ of the normal and $a$ are both positive integers,then the pair $(a, m)$ is