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Find the area enclosed by the ellipse,

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x^2/25+y^2/16=1 in the first quardent only?
asked Nov 11, 2014 in PRECALCULUS by anonymous

1 Answer

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The equation of ellipse is 

Now compare the given ellipse with the general form of ellipse .

General form of ellipse is 

Now solve for y

The part of ellipse in the first quadrant is positive .

Ellipse is symmetric with respect to both axes , the total area A is four times the area in the first quadrant .

So image

image

Let x = 5 sin ϴ

dx = 5 cos  ϴ

Now change the limits

When x = 0 , sin ϴ = 0 so ϴ = 0 .

When x = 5 ,sin ϴ = 1 so ϴ = π/2 .

image

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So the area of the ellipse in the first quadrant is 20π .

answered Nov 11, 2014 by yamin_math Mentor

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