$x - 2 = t^2$ and $y = 2t$ are the parametric equations of which parabola?

If $P$ is a point on the parabola $y^2=8x$ and $A$ is the point $(1,0)$,then the locus of the mid-point of the line segment $AP$ is

If the length of the latus rectum of a parabola,whose focus is $(a, a)$ and the tangent at its vertex is $x+y=a$,is $16$,then $|a|$ is equal to.

If $0 \leq x \leq 5$,then the minimum distance from the point $(0, c)$ to the parabola $y = x^2$ is:

Let $\alpha_1$ and $\alpha_2$ be the ordinates of two points $A$ and $B$ on a parabola $y^2=4ax$ and let $\alpha_3$ be the ordinate of the point of intersection of its tangents at $A$ and $B$. Then,$\alpha_3-\alpha_2=$

The angle of intersection between the curves $x^2 = 8y$ and $y^2 = 8x$ at the origin is