Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

Asked by maham237 @ in Mathematics viewed by 418 People

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. (2 points)
A. f(x) = − one fourth x2

B. f(x) = one fourth x2

C. f(x) = −4x2

D. f(x) = 4x2

Answered by maham237 @


The vertex is at (0, 0), halfway between the focus and directrix. This distance from focus to vertex (p) is 1 unit. The equation can be written as
f(x) = 1/(4p)(x -0)²
or
f(x) = (1/4)x²

This corresponds to the second selection,
B. f(x) = (1/4)x²

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