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

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apologiabiology

(y-k)²=4p(x-h)
(h,k) is vertex
and since we got the y term squred, it is facing left or right
when p is positive, then focus is to right of veretx
p is distance from focus to vertex and from vertex to dirextix

y²=-x
(y-0)²=4(-1/4)(x-0)
vertex is (0,0)
p is negative so then focus to left of vertex
so the focus is (-1/4,0)
dirextix is x=1/4

MrRoyal

The coordinate of the focus is (-1/9,0) and the equation of the directrix is x = 1/9

The equation of the parabola is given as:

\(y^2= -x\)

Rewrite the equation as:

\((y - 0)^2= -(x - 0)\)

The equation can be further rewritten in several ways.

One of them is:

\((y - 0)^2= 9 * -\frac 19(x - 0)\)

In the above equation,

The coordinate of the focus is (-1/9,0) and the equation of the directrix is x = 1/9

Read more about parabola at:

https://brainly.com/question/4061870

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