The focal distance of the point $(4, 4)$ on the parabola with vertex at $(0, 0)$ and symmetric about the $y$-axis is:

If the vertices of a triangle are $(am_1^2, 2am_1), (am_2^2, 2am_2),$ and $(am_3^2, 2am_3),$ then the area of the triangle is

The equation of the parabola whose focus is $(5, 3)$ and directrix is $3x - 4y + 1 = 0$ is:

The number of normals that can be drawn through the point $(2,0)$ to the parabola $y^2=7x$ is

If the equation of a system of parallel chords of the parabola $y^2 = \frac{2}{3}x$ is $y + 2x + 1 = 0$,find its diameter.

Let $P$ and $Q$ be points on the parabola $y^{2}=4x$ such that the line segment $PQ$ subtends a right angle at the vertex. If $PQ$ intersects the axis of the parabola at $R$,then the distance of the vertex from $R$ is