If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

The locus of a point such that two tangents drawn from it to the parabola $y^2 = 4ax$ are such that the slope of one is double the other is:

The tangent at the point $(1, 2)$ to the curve $y^2 = 4x$ makes an angle $\theta$ with the positive direction of the $X$-axis. Then $\theta =$ (in $^{\circ}$)

The parametric equations of the parabola $y^2-8x-4y-12=0$ are

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

Let $l$ be the directrix of the parabola $9y^2+12y+9x-14=0$ and $l_1$ be the line passing through the vertex of this parabola and the origin. If $(h, k)$ is the point of intersection of $l$ and $l_1$,then $h+k=$