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

An equilateral triangle is inscribed in the parabola $y^2 = 8x$,with one of its vertices at the vertex of the parabola. Then,the length of the side of that triangle is

The point on the parabola $y^2 = 8x$ at which the normal is parallel to the line $x - 2y + 5 = 0$ is

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$; focus $(3, 0)$.

$(1, 1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola,then $a+b+c+d=$

The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(3, 2)$ is . . . .