Question

Find the vertex, focus, directrix, and focal width of the parabola. x = 10y^2

Answer 1

vertex will be (0,0)

the stand form will be x/10=Y^2

the directrix is x=10

focus is (x+p,y) (1/40,0)

w=1/10

Answer 2

Vertex will be (0,0), the directrix is x=-1/40

the focus is (1/40, 0)

1/10 is focal width

Explanation:

Vertex will be (0,0), and the parabola will open to the right.

The standard form will be x/10 = y^2, so we know that 4p = 1/10, and that p = 1/40.

Your directrix will be x=0-p, so the directrix is x=-1/40

The focus is (x+p, y), so the focus is (1/40, 0)

At x = 1/40, y^2 = 1/400, so y = +/- 1/20. So 1/2 your width is 1/20. 2*(1/20) = 1/10 is your width at the focus.