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Asked Nov 22, 2019
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Area of an Ellipse In class we used A = Tab for the Area of an ellipse with
2.
a semimajor axis a and a semiminor axis b. Prove this result.
Hint: You may use parametric form of an ellipse: x a cos and y = bsin d.]
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Area of an Ellipse In class we used A = Tab for the Area of an ellipse with 2. a semimajor axis a and a semiminor axis b. Prove this result. Hint: You may use parametric form of an ellipse: x a cos and y = bsin d.]

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Step 1

Let the area of an ellipse is denoted by A.

Derive the equation of an ellipse by the given parametric equation.

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x acos,ybsinø cos2 +sin2 2 a 2 y= b

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Step 2

By calculating the area of the quarter of an ellipse and then multiply it by 4 will get us the desired ...

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A = ydx -4 2 dx a2 а 4b 2 0 a

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