SOLUTION: find the area bounded by the curve x^2=8y and its latus rectum

Question 1086398: find the area bounded by the curve x^2=8y and its latus rectum
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
The equation of the parabola can be written
Graphed below (green line is latus rectum):
�

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For a (vertical) parabola with vertex @(h,k):
Vertex is at (0,0) so h=k=0: so this parabola has equation
Solve for p (the distance from vertex to focus) by comparison: ==> ==> p=2
So focus is at (0,2). Latus rectum passed through (0,2) and intersects parabola where or (-4,2) and (4,2)
Using just the first quadrant & symmetry with 2nd quadrant:
Area =
= evaluated at 4 and 0
=
=
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