Question

What is an equation of the parabola with vertex at the origin and focus (0, 0.75)?

Answer 1

`x^(2) =3y`

Explanation:

Notice that the focus is a points on the vertical axis, that means the parabolla opens vertically, and has the form

`x^(2) =4py`

Because the parameter
`p` is positive and equal to 0.75. Additionally, the vertex is at the origin, that's why the equation is this simple.

Replacing the parameter value, we have

`x^(2) =4(0.75)y\\x^(2) =3y`

Therefore, the equation of a parabolla with vertex at the origin and focus at (0, 0.75) is
`x^(2) =3y`.