SOLUTION: hello! im doing conic sections and on my homework its asking me to graph {{{x+4+y^2-8y=o}}} im very lost if someone can help me slove this example it would be very helpful.

Question 599918: hello! im doing conic sections and on my homework its asking me to graph im very lost if someone can help me slove this example it would be very helpful.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
x+4+y^2-8y=0
complete the square
x+4+(y^2-8y+16)=16
x+4+(y-4)^2=16
(y-4)^2=16-x-4
(y-4)^2=-x+12
(y-4)^2=-(x-12)
This is an equation for a parabola that opens leftwards.
Its standard form: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of vertex
For given parabola:
vertex: (12,4)
axis of symmetry: y=4
4p=1
p=1/4
focus:(12-p,4)=(12-1/4,4)=(47/4,4) (p-distance left of vertex)
directrix: x=(12+p)=(12+1/4)=49/4 (p-distance right of vertex on axis of symmetry)
see graph below:
y=�(-x+12)^.5+4

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