Question 400901
graph the equation. identify the focus and directrix of the parabola, y^2=-4x
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y^2=-4x is of the form, y^2=-4px
This is a parabola with horizontal axis of symmetry,y=0, opening leftward.
vertex (0,0)
4p=4
p=1
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The focus is on the line of symmetry so its y-coordinate=0
Its x-coordinate is "p" or 1 unit to the left of the vertex.
Therefore, the (x,y) coordinates of the focus is (-1,0)
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The directrix is a vertical line "p" or 1 unit on the right side of the vertex, that is, x=1
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ans: The focus is at (-1,0), and equation of the directrix is x=1

see the following graph

{{{ graph( 300, 200, -6, 5, -10, 10, (-4x)^.5,-(-4x)^.5) }}}