# Calculus

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The equation of an ellipse centered at the origin is
(x^2/a^2) + (y^2/b^2)=1
The area of the upper half of the ellipse can be determined by finding the area between the ellipse and the x-axis (y=O). The total area of the ellipse is twice the area of the upper half.
(a) Solve the equation of the ellipse for y.(You will obtain two solutions,since there are two y values on the ellipse at every x value). Verify that the positive y values are returned by
y=b/a*square root -(x^2)+a^2

• Calculus -

solve for y:

y^2/b^2=1-x^2/a^2

y= +-b(sqrt(1-x^2/a^2))

if you want the form of the equation at end, multiply the right side by a/a
y= +-b/a sqrt(a^2-x^2)

Now verify by putting this into the original equation.

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