SOLUTION: Find the center,vertices, foci, and asymptotes of the hyperbola 4x2-y2-8x+2y-1=0 and draw a graph. Find the vertex, focus, and directrix of the parabola x2-4x-4y+16=0. graph th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the center,vertices, foci, and asymptotes of the hyperbola 4x2-y2-8x+2y-1=0 and draw a graph. Find the vertex, focus, and directrix of the parabola x2-4x-4y+16=0. graph th      Log On


   

Question 52470: Find the center,vertices, foci, and asymptotes of the hyperbola 4x2-y2-8x+2y-1=0 and draw a graph.
Find the vertex, focus, and directrix of the parabola x2-4x-4y+16=0. graph
thank you very much

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex, focus, and directrix of the parabola x^2-4x-4y+16=0
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Rewrite as x^2-4x+? = 4y+16+?
Complete the square:
x^2-4x+4 = 4y+20
(x-2)^2=4(1)(y+5)
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Vertex at (2,-5).
Since 4p=4, p=1
Focus = (2,-5+1)= (2,-4)
Directrix is y=-5-1=-6
Cheers,
Stan H.