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.

The locus of the mid-point of the line segment joining the focus of the parabola $y^{2}=4ax$ to a moving point of the parabola,is another parabola whose directrix is

The angle of intersection between the curves $y^2 = 4x$ and $x^2 = 32y$ at the point $(16, 8)$ is:

Statement $- 1 :$ For all non-zero values of $m$,$y = mx - 1/m$ is always a tangent to the parabola $y^2 = -4x$.
Statement $- 2 :$ Every tangent to the parabola $y^2 = -4x$ touches its axis at a point whose $x$-coordinate is non-negative.

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the value of $k$ is

If $a \ne 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$,then