Question

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

Answer 1

A parabola can be represented by the equation y^2 = -x. The focus is located at (-1/16, 0) and the equation of the directrix is x = 1/16.

Step-by-step explanation:

The given equation y2 = -x represents a parabola.

To find the coordinates of the focus and the equation of the directrix, we can compare the given equation to the standard form of a parabola y2 = 4px (with the vertex at the origin).

In this case, we have y2 = -x which can be rewritten as y2 = -4(1/4)x, showing that 4p = -1/4.

From this, we can determine that the focus is located at (p, 0), so the focus is at (-1/16, 0). The equation of the directrix is given by x = -p, so the directrix is the line x = 1/16.

Answer 2

(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