SOLUTION: Given the parabola having the equation x^2+4y+8x=4, find the vertex, focus, and the length of the latus rectum. Sketch the graph.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Given the parabola having the equation x^2+4y+8x=4, find the vertex, focus, and the length of the latus rectum. Sketch the graph.      Log On


   

Question 1170337: Given the parabola having the equation x^2+4y+8x=4, find the vertex, focus, and the length of the latus rectum. Sketch the graph.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B8x=4-4y
x%5E2%2B8x%2B16=4-4y%2B16
%28x%2B4%29%5E2=-4y%2B20
highlight%28%28x%2B4%29%5E2=-4%28y%2B5%29%29

The equation now shows parabola is concave downward with vertex as maximum point.

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Vertex (-4,-5)
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Distance between vertex and either focus or directrix is 1.
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Focus (-4,-6)
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Directrix y=-4
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graph%28500%2C500%2C-10%2C4%2C-10%2C4%2C-%281%2F4%29%28x%2B4%29%5E2-5%29