If $A(2, 0)$ is the vertex and the $y-$axis is the directrix of a parabola, then its focus is

An equilateral triangle is inscribed in a parabola $y^2=4ax$, whose vertex is at the vertex of the parabola. The length of each side of the triangle is 

The focal distance of a point $P$ on the parabola $y^2 =12x$ is $4$. The abscissa $P$ is

The equation of a parabola with vertex at $O(0, 0)$ and focus at $F(0, 2)$ is

A parabola has its vertex at the origin; its axis lies along the $x-$axis and it passes through the point $P(2, 3)$. The equation of the parabola is

A parabola has its vertex at the origin and passes through the point $P(3,-4)$ and it is symmetric about the $y-$axis. Its equation is

The equation of an ellipse is $\frac{x^2}{16}+\frac{y^2}{9}=1$. Find

Length of the major axis = _____units.

Length of the minor axis =_____units.

Coordinates of its vertices are $A$(_____) and $B$(_____).

Coordinates of its foci are $F_1$(_____) and $F_2$(______).

Eccentricity, $e=$_____.

Length of the latus rectum =_____units.

The equation of an ellipse is $4x^2 +9y^2 =144$. Find: Length of the major axis, Length of the minor axis, Coordinates of its vertices, Coordinates of its foci, Eccentricity and Length of the latus rectum.