Question

determine the focus for the equation y=x^2

Answer 1

In y = ax^2, a = 1. But a = 1/(4p), where p is the distance from the vertex to the focus.

So 1 = 1/4p

4p = 1

p = 1/4

The focus is 1/4 of a square up from the vertex inside the parabola at (0, 1/4).

The directrix would then be 1/4 of a square below the vertex at y = -1/4.

Answer 2

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