Question

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

Answer 1

Answer:

$x^{2} =3y$

Step-by-step 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 $x^{2} =3y$.