The length of the latus rectum of the parabola $x^{2}+2y=8x-7$ is

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola $y^2 = 4ax$ is another parabola with the directrix

Normals are drawn from the point $P(8,0)$ to the parabola $y^2=12x$. If $\theta$ is the acute angle between two non-horizontal normals among them,then $\tan \theta=$

What is the focus of the parabola $4y^2 + 12x - 20y + 67 = 0$?

The axis of a parabola is along the line $y=x$. The distance of its vertex $A$ from $(0,0)$ is $\sqrt{2}$ and that of its focus $S$ from $(0,0)$ is $2\sqrt{2}$. If $A$ and $S$ lie in the first quadrant,then the equation of the parabola in parametric form is

The normal at the point $(bt_1^2, 2bt_1)$ on the parabola $y^2 = 4bx$ meets the parabola again at the point $(bt_2^2, 2bt_2)$. Then: