Two tangents are drawn from a point $(-2, -1)$ to the curve $y^2 = 4x$. If $\alpha$ is the angle between them,then $|\tan \alpha|$ is equal to:

Which one of the following curves cuts the parabola $y^2 = 4ax$ at right angles?

For a parabola with focus $(2, 1)$ and directrix $2x - 3y + 1 = 0$,what is the equation of the latus rectum?

The parametric equations of the parabola $y^2 - 12x - 2y - 11 = 0$ are:

From an external point $P(h, k)$,a pair of tangent lines are drawn to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the inclinations of these tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,then the locus of $P$ is:

If all the vertices of an equilateral triangle lie on the parabola $y^2=16x$ and one of them coincides with the vertex of that parabola,then the length of the side of that triangle is