parabolas 5

Question

Find the vertex, focus, directrix, and focal width of the parabola. 

x² = 28y

Answer 1

The parabola equation is

In the equation the x part is squared, so the parabola is vertical parabola.

Standard form of vertical parabola is

Where vertex is (h , k), focus at (h, k + p) and directrix is y = k - p

Compare it to above standard form.

p = 7

Since p > 0 , the parabola opens upward.

Vertex ( 0,0)

Focus (k, k + p) = (0, 0 + 7)

Focus = (0, 7)

Directrix is y = k - p

y = 0 - 7

Directrix is y = - 7

Focal width 4p = 28.