SOLUTION: Find the standard equation with focus: (-2,0) and Directrix: x=4 (y-k)2 = -4p(x-h) This is as far as I have gotten. I think that the vertex is (1,0)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the standard equation with focus: (-2,0) and Directrix: x=4 (y-k)2 = -4p(x-h) This is as far as I have gotten. I think that the vertex is (1,0)      Log On


   

Question 449489: Find the standard equation with focus: (-2,0) and Directrix: x=4
(y-k)2 = -4p(x-h) This is as far as I have gotten. I think that the vertex is (1,0)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the standard equation with focus: (-2,0) and Directrix: x=4
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Since the focus is to the left of the directrix, this is a parabola which opens leftward with axis of symmetry being the x-axis or y=0. Standard form for this parabola is:
y^2=-4px
Distance between focus on the axis of symmetry=6
p=1/2 this distance = 3
vertex on the axis of symmetry is at (1,0) (located halfway between focus and directrix on axis of symmetry)
Equation of given parabola:
y^2=-12(x-1)
see the graph below for a visual representation of the equation for given parabola.
y=(-12(x-1))^.5