$A$ parabola having its axis parallel to the $Y$-axis passes through the points $(0, 2/5)$,$(4, -2)$,and $(1, 8/5)$. Which of the following points lies on this parabola?

If $a$ and $c$ are the segments of a focal chord of a parabola and $b$ is the semi-latus rectum,then:

Find the equation of the parabola whose axis is parallel to the $y$-axis and which passes through the points $(0,4), (1,9)$ and $(4,5)$.

Let a parabola $P$ be such that its vertex and focus lie on the positive $x$-axis at a distance $2$ and $4$ units from the origin,respectively. If tangents are drawn from $O(0,0)$ to the parabola $P$ which meet $P$ at $S$ and $R$,then the area (in $sq. \text{ units}$) of $\triangle SOR$ is equal to:

If the tangent and normal at any point $P$ of a parabola meet the axis of the parabola in $T$ and $G$ respectively,then

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