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 Aug 27 revised How can I describe the area between two ellipses? added 161 characters in body Aug 27 comment How can I describe the area between two ellipses? No. This is a problem I made up. I understand the approach that you have, but, unfortunately, it is not finding the area of the region $\Sigma$ that I'm interested in, it's more about defining it. I am more interested in finding a definition of $\Sigma$ with $u$ and $v$. Aug 27 revised How can I describe the area between two ellipses? Resolved one of my questions, formatting Aug 27 comment How can I describe the area between two ellipses? FYI - The image I posted used (1) $\frac{(x-5)^2}{3^2}+\frac{y^2}{6^2}=1$ and (2) $\frac{(x-7)^2}{12}+\frac{y^2}{3^2}$. Should I put that in there? Aug 27 comment How can I describe the area between two ellipses? @BenCrowell I agree with Lubin - most likely, the term $(1-\frac{(x_0-c_2)^2}{x_1^2})$ in $y_0=\sqrt{y_2^2(1-\frac{(x_0-c_2)^2}{x_1^2})}$ becomes negative, causing the smaller $x$ values to become imaginary. Therefore, the $x$ that we're looking at has to be the larger one. I guess that answers that. I don't think we need to go through a numerical case if my explanation sounds convincing enough. That still only gets me down to where I ended in my question, though. Aug 27 asked How can I describe the area between two ellipses? Aug 26 comment Numerical Analysis There was no complex conjugate. Just saying. Aug 26 answered Can you approximate a vector field? Aug 26 revised Calculate the area on a sphere of the intersection of two spherical caps added 173 characters in body Aug 26 revised Calculate the area on a sphere of the intersection of two spherical caps Minor LaTeX corrections, grammar Aug 26 revised Calculate the area on a sphere of the intersection of two spherical caps Minor LaTeX corrections Aug 26 answered Calculate the area on a sphere of the intersection of two spherical caps Aug 25 comment Divisibility of consecutive natural numbers @dato yes but what anon is trying to convey here is that there doesn't have to be a prime every 2012 consecutive numbers. Aug 25 accepted Solving the DE for a two-body system Aug 24 comment Pre-Calculus - Solving for $x^3$ When you used the quadratic formula and got the two roots $a=\frac{-1+i\sqrt{3}}{2}$ and $b=\frac{-1-i\sqrt{3}}{2}$ you should be replacing $x^2+x+1$ with $(x-a)(x-b)$, not what you did. Aug 24 revised Green's theorem for conservative fields - are partials equal? Minor math error (forgot dA) Aug 24 comment Green's theorem for conservative fields - are partials equal? No problem. Glad to help. FYI, subscripts, in this context, mean partials - $\frac{\partial f}{\partial x}=f_x$. Aug 24 comment Integer combination Will the formula always be less than or equal to? And that simple? (i.e., in the form $a x + b y \le c$ for integers a, b, and c)? Aug 24 comment Green's theorem for conservative fields - are partials equal? There. I hope my edit was what you were looking for. Aug 24 revised Green's theorem for conservative fields - are partials equal? Missed a period, added a proof, put more LaTeX in.