Square ABCD has side length 60. An ellipse E is circumscribed about the square and there is a point P on the ellipse such that PC = PD =50. What is the area of E?

I got to the part with the point (30, 30). Now what next?

6 answers

If you draw the figure, you will see that the ellipse has semi-major axis of 30+40=70

So, the equation of the ellipse is

x^2/70^2 + y^2/b^2 = 1

Since (30,30) is on the ellipse,

30^2/70^2 + 30^2/b^2 = 1
b = 21√(5/2)

The area of the ellipse is thus

A = πab = 735π√10

735π√10

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