How to find the circumference of an Ellipse?

I only know the dimensional formulas(Chapter named conic section, something like x1/a^2 + x2/b^2), but not the metrical measurement and what no.

It's an extremely complicated process, involving integrals. >_>; Eh. You also have that wrong. =X

Ellipses are circles where x

^{2} and y

^{2} have different coefficients. In general, the equation of a circle is:

x

^{2} + y

^{2} = r

^{2}This can also be written as:

^{x2}/

_{r2} +

^{y2}/

_{r2} = 1

For an ellipse, the general equation is given by:

^{x2}/

_{a2} +

^{y2}/

_{b2} = 1

where a is the "horizontal radius" and b is the "vertical radius"

The circumference is...

4aE(e

^{2})

where e is the eccentricity and is equal to:

e = sqrt( 1 - (

^{b}/

_{a})

^{2} )

and E is something called an Elliptical Integral, which >_> I don't really understand, so I can't help with that one. Basically, it's an integral that doesn't work out too nicely and needs to be solved with infinite series.

All of this adds up to say that you should probably not bother finding the circumference of an ellipse. <_____<;;

Oh joy. I had forgotten that conics are gotten by intersecting a cone with a plane. I have a bad feeling we're gonna be going into them in Calc 3. >_>;

OH OH. Here are a couple of questions from my Calc 3 test yesterday! I wonder if anybody can solve them~

The temperature at any point (x,y) on a steel plate is given by T = (y) / (x

^{2} + y

^{2}) where x and y are measured in meters. At the point (2,1), find the rate of change of the temperature with respect to the distance moved along the plate in the y direction.

Suppose w = sqrt( x

^{2} + y

^{2} ), with x = sin2t and y = 3e

^{t}cos2t. Find the value of

^{dw}/

_{dt} when t = 0.

I was supposed to use the Calc 3 Chain Rule for that^ :O

I picked the two... "easiest" ones, since they just involve differentiation.