Michael J. answered • 06/19/16
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Mastery of Limits, Derivatives, and Integration Techniques
To find the area of the ellipse is to find the area of the under the curve. This means that you need to find the definite integral of the function y with respect to x.
First, find the x-intercepts of this equation. The x-intercepts will serve as your bounds.
Then, you will solve for y explicitly from the equation of the ellipse.
Lastly, you will take the integral of y with respect to x. You will evaluate the definite integral using the bounds. The negative x-intercept will be your lower bound. The positive x-intercept will be your upper bound.
As a last step, multiply the result of the definite integral by 2.
Got it!
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
Kenneth S.
06/19/16