What is the slope of the tangent drawn from the point $(4, 10)$ to the parabola $y^2 = 9x$?

The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

Find the length of the tangent drawn from an endpoint of the latus rectum of the parabola $y^2 = 4ax$ to a circle of radius $a$ that touches the parabola at its vertex.

Suppose $AB$ is a focal chord of the parabola $y^2=12x$ of length $l$ and slope $m < \sqrt{3}$. If the distance of the chord $AB$ from the origin is $d$,then $l \cdot d^2$ is equal to ....................

If one end of a focal chord of the parabola $y^2 = \frac{8}{a} x$ $(a > 0)$ is at $(1, 4)$,then the length of this focal chord is

The point of intersection of the latus rectum and the axis of the parabola ${y^2} + 4x + 2y - 8 = 0$ is: