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Question 126420This question is from textbook
: i really need help with this problem i tried it but it didnt work out. it says an ellipse with center at the origin and horizontal major axis is to fit snugly inside a rectangle that has its longer sides horizontal. the area of the rectangle is 12 square units, and the perimeter is 14 units. find an equation for the ellipse.
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! an ellipse with center at the origin and horizontal major axis is to fit snugly inside a rectangle that has its longer sides horizontal. the area of the rectangle is 12 square units, and the perimeter is 14 units. find an equation for the ellipse.
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Find the length and width of the rectangle:
2(length + width) = 14
l + w = 7
lw = 12
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l=7-w
(7-w)w = 12
-w^2+7w=12
w^2-7w+12=0
(w-3)(w-4) = 0
w = 3, then length = 4
OR
w = 4, then length = 3
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The longer side is horizontal so must be 4.
The shorter side must be 3.
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The semi-major axis must be 2.
The semi-minor axis must be 1.5
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Equation of the ellipse:
x^2/2^2 + y^2/1.5^2 = 1
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Cheers,
Stan H.
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