Find the area enclosed by the ellipse,

Question

x^2/25+y^2/16=1 in the first quardent only?

Answer 1

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 

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 .

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