If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9x$,then:

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

The length of the latus rectum of the parabola ${y^2} = 5x + 4y + 1$ is

Find the angle of intersection between the curves $y^2 = 4ax$ and $x^2 = 4ay$.

What is the area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola $x^2 = 8y$?

Let $E$ denote the parabola $y^2=8x$. Let $P=(-2,4)$,and let $Q$ and $Q^{\prime}$ be two distinct points on $E$ such that the lines $PQ$ and $PQ^{\prime}$ are tangents to $E$. Let $F$ be the focus of $E$. Then which of the following statements is (are) $TRUE$?
$(A)$ The triangle $PFQ$ is a right-angled triangle
$(B)$ The triangle $QPQ^{\prime}$ is a right-angled triangle
$(C)$ The distance between $P$ and $F$ is $5\sqrt{2}$
$(D)$ $F$ lies on the line joining $Q$ and $Q^{\prime}$