Area of an ellipse using linear algebra

[JellyFish]

I am supposed to find the area of the ellipse( [x[sup:w4qzbo94]2[/sup:w4qzbo94]]/16) + ([y[sup:w4qzbo94]2[/sup:w4qzbo94]]/25) = 1 using linear algebra only...no calculus or anything else.

I guess if I find a linear transformation that takes x[sup:w4qzbo94]2[/sup:w4qzbo94] + y[sup:w4qzbo94]2[/sup:w4qzbo94] = 1 to the equation above this could work....but I'm not sure what it would be.

Thanks for taking a look at this problem.

 

[Denis]

Go here (you'll see how simple it is): http://www.math.hmc.edu/funfacts/ffiles/10006.3.shtml