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

1 Answer
Jun 26, 2018

Answer:

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!