If the focus of a parabola is $(3, 0)$ and the length of its latus rectum is $8$,what is its vertex?

If $x = my + c$ is a normal to the parabola ${x^2} = 4ay$,then the value of $c$ is

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$

The Cartesian coordinates of the point on the parabola $y^{2}=x$ whose parameter is $t = -\frac{4}{3}$ are

Let $A, B$ and $C$ be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through $C$ parallel to the $x$-axis at the point $D$. Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$. Then $\left(\frac{AM \cdot BN}{CD}\right)^2$ is equal to...........

The locus of the orthocentre of the triangle formed by the focal chord of the parabola $y^2 = 4ax$ and the normals drawn at its extremities is