Question 848901: Find the focus, vertex, directrix , axis, and latus rectum of the parabola, y2 =8x-8y
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the focus, vertex, directrix , axis, and latus rectum of the parabola, y2 =8x-8y
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y2 =8x-8y
y^2+8y=8x
complete the square:
y^2+8y+16=8x+16
(y+4)^2=8(x+2)
This is an equation of a parabola that opens rightward.
Its basic equation: (y-k)^2=4p(x-h)
vertex: (-2,-4)
axis of symmetry: y=-4
4p=8
p=2
focus: (0,-4) (p-distance to the right of the vertex on the axis of symmetry)
directrix: x=-4 (p-distance to the left of the vertex on the axis of symmetry)
latus rectum or focal width=4p=8
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