# A parabola can be represented by the equation y2 = –x. What are the coordinates of the focus and the equation of the d

Question

A parabola can be represented by the equation y2 = –x.

What are the coordinates of the focus and the equation of the directrix?

focus: (negative one-fourth, 0); directrix: x = One-fourth
focus: (one-fourth, 0); directrix: x = Negative one-fourth
focus: (–4,0); directrix: x = 4
focus: (4,0); directrix: x = –4

in progress 0
4 weeks 2023-01-07T18:07:54+00:00 1 Answer 0 views 0

1. The coordinates of the focus and the equation of the directix are F(x, y) = (- 1 / 4, 0) and x = 1 / 4, respectively.

### What are the coordinates of the focus and the equation of the directrix of a given parabola?

According to the statement, we find a parabola of the form (y – k)² = 4 · p · (x – h), where p is the distance from the vertex to the focus. The formulae for its focus and the directrix are:
Focus
F(x, y) = (h + p, k)
F(x, y) = (0 – 1 / 4, 0)
F(x, y) = (- 1 / 4, 0)
Directrix
x = h – p
x = 0 – (- 1 / 4)
x = 1 / 4
Then, the coordinates of the focus and the equation of the directix are F(x, y) = (- 1 / 4, 0) and x = 1 / 4, respectively.