Question

Find an equation for the parabola that has its vertex at the origin and satisfies the given condition.Focus F(0, - 9/4)

Answer 1

You have to find the equation for the parabola and you have that the vertex is (0,0) and the focus is (0,-9/4).

We should notice that the focus is on the line x=0, then the parabola has the following form.

Notice that the formula for the parabola is

$(x-h)^2=4p(y-k)$

where the focus is (h,k+p) and the directriz is y=k-p. In our case h=0, k=0. Then

$x^2=4py$

then

$p=4(\frac{-9}{4})=-9$

Then the formula for the parabola is

$x^2=-9y$