The distance between the vertex and the focus of the parabola $x^2-2x+3y-2=0$ is

The condition that the parabolas $y^2 = 4ax$ and $y^2 = 4c(x - b)$ have a common normal other than the $x$-axis ($a, b, c$ being distinct positive real numbers) is

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2, y=10t+4$ (where $t$ is a parameter) are

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

The lengths of the two focal chords of the parabola $y^2 = 16x$ are $25$ units each. If these two chords cut the parabola at $A, B, C$ and $D$,then the area (in sq. units) of the quadrilateral formed by $A, B, C$ and $D$ 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 $\text{ unit}^{2}$)