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