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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

Respuesta :

sqdancefan
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

The equation of the parabola is,[tex]f(x) = (1/4)x^2[/tex]

We have given that the vertex is at (0, 0),

halfway between the focus and directrix.

This distance from focus to vertex (p) is 1 unit.

what is the equation of the directrix?

The equation of the directrix is x=h-p

The equation can be written as,

[tex]f(x) = 1/(4p)(x -0)^[/tex]

or

 [tex]f(x) = (1/4)x^2[/tex]

Therefor the equation of the parabola is,

[tex]f(x) = (1/4)x^2[/tex]

To learn more about the equation of the parabola  visit:

https://brainly.com/question/4148030

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