Question

vince33 Could you please do your homework by yourself, or wolfram alpha?
Also, my question is, find the area of a general ellipse in the form with the xy term using integration and trig substitution.

Answer 1

well area of ellipse = pi*a*b, where a and b are major and minor axis

Answer 2

Hmm. Can you show your work please?

Answer 3

you want area in terms of x,y ?

Answer 4

Actually, scratch that. I need a hint as to how to transform an ellipse into one with no rotation.

Answer 5

http://en.wikipedia.org/wiki/Rotation_%28mathematics%29#Matrix_algebra

Answer 6

Wait, what's the equation of a rotated ellipse?

Answer 7

to answer prev question regarding proof of area
the equation for general ellipse solved for y
\[y = \pm \frac{b}{a}\sqrt{a^{2}-x^{2}}\]
due to symmetry, we can integrate to get area in 1st quadrant, then multiply by 4
\[A = 4\frac{b}{a}\int\limits_{0}^{a}\sqrt{a^{2}-x^{2}} dx\]
set x = asin(u)
dx = acos(u)

Answer 8

dumb, I got the integration, don't spoil it xD

Answer 9

haha ok
the equation for rotated ellipse, you replace x and y with x' and y' based on formulas which depend on angle of rotation

Answer 10

but the problem is I want the general area given in terms of coefficients. I wanted to do a translation and rotation to make it at the origin, then integrate for area. Is that possible>

Answer 11

so you are starting with a slanted ellipse and want the area in terms of coefficients.
yes you would have to rotate it so its standard ellipse on xy axis
then just determine what a and b are

Answer 12

yes. But how would I know what the general equation of the slanted ellipse was?

Answer 13

oh its not given?

Answer 14

its usually of the form
\[\frac{(x \pm y)^{2}}{c}+\frac{(x \pm y)^{2}}{d} = 1\]
but it depends on the angle

Answer 15

there probably is a general form for slanted ellipse in terms of theta but i don;t know what it is

Answer 16

here we go
http://en.wikipedia.org/wiki/Ellipse#General_ellipse

Answer 17

so from that general equation, replace x and y with x' and y'
solve for y' and integrate
are we given the angle?
or will the area be in terms of theta?

this could get messy