Question

How do you find the equation of a parabola with vertex at the origin and focus (2,0)?

Answer 1

See below for an explanation!

Explanation:

Since the focus is to the right of the parabola's vertex on a graph, and since the focus is always contained within the parabola, the parabola faces right. The formula for a right-facing parabola is

`x-h=1/(4p)(y-k)^2`

Since the vertex is the origin, there aren't any `h` or `k` values:

`x=1/(4p)y^2`

You may know that `p` is the distance from the vertex of a parabola to both its focus and directrix. The focus is 2 units away, so `p=2`. Because of this, the scale factor would be `1/(4*2)=1/8`. Our final equation is

`x=1/8y^2`

Hope this helped. Have a nice day!