The coordinates of a moving point $P$ are $(2t^2+4, 4t+6)$. Then its locus will be a

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(2, 3)$,and the axis is along the $x$-axis.

If the point on the curve $y^{2}=6x$,nearest to the point $\left(3, \frac{3}{2}\right)$ is $(\alpha, \beta)$,then $2(\alpha+\beta)$ is equal to $.....$

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,$\alpha_3-\alpha_2=$

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

The locus of the mid-point of the line segment joining the focus and any point on the parabola $y^{2}=4ax$ is a parabola. Find the equation of its directrix.