The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point $(2,0)$ to the parabola $2y^{2} = -x$. If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x-5)^{2} + y^{2} = r$,then $17r$ is equal to.

If the parabolas $y^2 = 4b(x - c)$ and $y^2 = 8ax$ have a common normal,then which one of the following is a valid choice for the ordered triad $(a, b, c)$?

If two tangents drawn from a point $P$ to the parabola $y^2 = 4x$ are such that the slope of one tangent is double the other,then $P$ lies on the curve:

If $ax + by = 1$ is a normal to the parabola $y^2 = 4px$, then the condition is:

The vertex and the focus of the parabola $2y^2 + 5x - 6y + 1 = 0$ are respectively