Sue M.

asked • 06/19/16

area of ellipse- calculus

find the area of the ellipse (x+2y)2 + (3x+4y)2 =1

1 Expert Answer

By:

Michael J. answered • 06/19/16

Tutor
5 (5)

Mastery of Limits, Derivatives, and Integration Techniques

Kenneth S.

The equation stated is going to have xy terms, and so there needs to be a suitable rotation of axes in order to get the equation in the standard form suitable for the recommended definite integration. 
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06/19/16

Michael J.

Let's see your solution.  I am interested to see what you come up with.
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06/19/16

Mark M.

When mutiplied out:
10x2 + 17y2 + 28xy + 0x + 0y + 0 = 1
For angle of rotation
cot(2θ) = (10 - 17) / 28
cot(2θ⌋) = 7/28
cot(2θ) = 0.25
tan(2θ) = 4
2θ = 75.96
θ = 37.98
 
For the equation of the rotated axis:
x' = x cos θ + y sin θ
y' = x sin θ + y cos θ
 
Determine the values of x' and y'. Substitute in to originals equation.
The resulting equation is the formula of the ellipse in relation to the rotated axis.
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06/19/16

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