Find the focus directrix focal diameter vertex and axis of s

Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola

68(y2)=(x+7)^2

Solution: Equation of the parabola 68(y2) = (x+7)^2.

Comparing this equation with the standard equation of parabola 4a(yk) = (x-h)^2, we get h=-7, k=2 and 4a = 68

or a = 17.

We know that focus (0,a) = (0, 17) or (x+7, y-2) = (0, 17) or x =-7, y=19.

Thus Focus = (-7, 19).

Equation of directrix is (y-k) = -a or (y-2) =-17 or y =-17+2 =-15

Vertex (h, k) = (2,-7).

Axis of symmetry is x+7=0 or x = -7.

Focal diameter = 4a = 4 (17).

Thus Focal diameter = 68. Ans

And directrix is y = -15.