If the line $y=2x+k$ is a normal to the parabola $y^2=4x$,then $k=$

Find the axis of the parabola $9y^2 - 16x - 12y - 57 = 0$.

If the line $lx + my + n = 0$ is a tangent to the parabola $y^2 = 4ax$,then the locus of its point of contact is

Variable chords of the parabola $y^2 = 4ax$ subtend a right angle at the vertex. Then:

Let $P(\alpha, \beta)$ be a point on the parabola $y^2 = 4x$ which is at minimum distance from the circle $x^2 + y^2 - 4x - 20y + 103 = 0$. Then $\alpha \beta$ is

If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9x$,then: