If the $x$-intercept of a focal chord of the parabola $y^2 = 8x + 4y + 4$ is $3$,then the length of this chord is equal to $.............$

The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^{2}$) of the triangle $PAB$ is:

The focus of the parabola $4y^2 - 6x - 4y = 5$ is

The point of contact of the tangent to the parabola $y^2 = 4ax$ which makes an angle of $60^\circ$ with the $x$-axis is:

$A$ chord is drawn through the focus of the parabola $y^2 = 6x$ such that its distance from the vertex of this parabola is $\frac{\sqrt{5}}{2}$. Then,its slope can be:

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...........