SOLUTION: Write the equation of a parabola that has a focus pointlocated at (-3,-1) and the equation of the directrix is y=3.
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Question 615730: Write the equation of a parabola that has a focus pointlocated at (-3,-1) and the equation of the directrix is y=3.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation of a parabola that has a focus pointlocated at (-3,-1) and the equation of the directrix is y=3.
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Given parabola opens downwards:
Its standard form of equation: (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of vertex
For given parabola:
x-coordinate of vertex=-3 (fm given focus coordinates)
y-coordinate of vertex=1 (halfway between focus and directrix on axis of symmetry, x=-3)
vertex: (-3,1)
p=2 (distance from directrix or focus to vertex on axis of symmetry)
4p=8
Equation of given parabola:
(x+3)^2=-8(y-1)
see graph below as a visual check:
y=-(x+3)^2/8+1
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