The tangents drawn from the ends of the latus rectum of the parabola ${y^2} = 12x$ meet at:

Let $A(4, -4)$ and $B(9, 6)$ be points on the parabola $y^2 = 4x$. Let $C$ be a point chosen on the arc $AOB$ of the parabola,where $O$ is the origin,such that the area of $\Delta ACB$ is maximum. Then,the area (in sq. units) of $\Delta ACB$ is

Find the locus of the midpoint of the chord of the parabola $y^2 = 4x$ drawn from the vertex.

Suppose $BOAC$ is a rectangle in the $XY$-plane where $O$ is the origin and $A, B$ lie on the parabola $y=x^2$. Then,$C$ must lie on the curve

Let $P$ represent the point $(3, 6)$ on the parabola $y^2 = 12x$. For the parabola $y^2 = 12x$,if $l_1$ is the length of the normal chord drawn at $P$ and $l_2$ is the length of the focal chord drawn through $P$,then $\frac{l_1}{l_2} = $

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(5, 2)$,and symmetric with respect to the $y$-axis.