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Question 593014: What is the focus, vertex, axis of symmetry and directrix of the parabola equation y2-8y+16x-64=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the focus, vertex, axis of symmetry and directrix of the parabola equation
y2-8y+16x-64=0
complete the square
(y^2-8y+16)+16x-64-16=0
(y-4)^2+16x-80=0
(y-4)^2=-16x+80
(y-4)^2=-16(x-5)
This is an equation for a parabola that open leftwards of the standard form: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex.
For given parabola:
4p=16
p=4
vertex: (5,4)
axis of symmetry: y=4
focus: (1,4) (p units to left of vertex on axis of symmetry)
directrix: x=9 (p units to right of vertex on axis of symmetry)
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