Question

determine the focus of this equation.

y=x^2

I GIVE MEDALS

Answer 1

is there a formula for the focus of a parabola?

Answer 2

no i dont think so

Answer 3

The answer is (0, 1/4) but I don't know how to derive it easily.
This is one bit that I have not had to use in the last 40 years.

Answer 4

written in this form: 4ay = x^2, 4a is your focal width (latus rectum). a represents the distance from your vertex to the focus (it is also the distance to the directrix in the opposite direction).

since your equation is y = x^2, 4a = 1. so a = 1/4.
so the focus for y=x^2 is at (0, 1/4)