Question 974490: What is the vertex, focus, and directrix of x=1/2y^2+3
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the vertex, focus, and directrix of
x=1/2y^2+3
2x=y^2+6
y^2=2x-6
y^2=2(x-3)
This is an equation of a parabola that opens rightward,
Its basic form: (y-k)^2=4p(x-h), (h,k)=coordinates of the vertex
For given parabola:
vertex: (3,0)
axis of symmetry: y=0
4p=2
p=2/4=1/2
focus: (3.5,0) (p-distance right of vertex on the axis of symmetry)
directrix: x= 2.5 (p-distance left of vertex on the axis of symmetry)
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