If a focal chord of the parabola $y^2 = 4ax$ makes an angle $\theta$ with its axis,then the length of the perpendicular from the vertex to this chord is......

If the line segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola makes an angle $\theta$ with the positive $X$-axis,then the length of that line segment is

Find the equation of the normal to the parabola $y^2 = 4x$ which is parallel to the line $y = 3x + 4$.

The lengths of the two focal chords of the parabola $y^2 = 16x$ are $25$ units each. If these two chords cut the parabola at $A, B, C$ and $D$,then the area (in sq. units) of the quadrilateral formed by $A, B, C$ and $D$ is

For a parabola with focus $(2, 1)$ and directrix $2x - 3y + 1 = 0$,what is the equation of the latus rectum?

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between $A$ and $B$,and $a$ denotes the area of $\triangle SAB$,where $S$ is the focus of the parabola $y^2=4x$,then the value of $(a+d)$ is: