If $(0, 4)$ and $(0, 2)$ are the vertex and focus of a parabola respectively,then what is its equation?

Variable straight lines $y=mx+c$ make intercepts on the curve $y^2-4ax=0$ which subtend a right angle at the origin. Then the point of concurrence of these lines $y=mx+c$ is

The focal distance of a point $(5, 5)$ on the parabola $x^2 - 2x - 4y + 5 = 0$ is

Find the area of the triangle formed by the points $(at_1^2, 2at_1)$,$(at_2^2, 2at_2)$,and $(at_3^2, 2at_3)$.

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

$TP$ and $TQ$ are tangents of the parabola $y^2 = 8x$ at $P$ and $Q$ respectively. If the chord $PQ$ passes through the point $(-2, 3)$ and the locus of point $T$ is $y = mx + c$,then $(m + c)$ is equal to -