Anthony Reverri
Section 27
Workshop 5
This week’s workshop asks us to find the area enclosed by two ellipses. The equations for
both ellipses are and. First we must put but of these equations in terms of.
From here there are many strategies to find the total area between these two ellipses. I am
going to briefly outline my approach, then explain the calculations. Since these ellipses are both
symmetrical across the
x
and
y
axis, solving for where they equal each other will give me the co
ordinates of all the intersections. With these coordinates, I can connect two of the points, and
then use the distance formula to find the length of one side. I can then square this length in order
to find the area of the square inside the middle of the ellipse. To avoid confusion, I will explain
how to find the rest of the area when we get to that step.
Start with finding where the equations intersect (can disregard sign).
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 Spring '08
 sc
 Calculus, Equations, Distance Formula, Anthony Reverri

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