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

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Khánh Gia 4 weeks 2023-01-07T18:07:54+00:00 1 Answer 0 views 0

Answer ( 1 )

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    2023-01-07T18:09:38+00:00
    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.
    To learn more on parabolas: https://brainly.com/question/21685473
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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )