Q. An equilateral triangle is inscribed in an ellipse whose equation is $x^2+4 y^2=4$. One vertex of the triangle is $(0,1)$, one altitude is contained in the $y$-axis, and the length of each side is $\sqrt{m / n}$, where $m$ and $n$ are relatively prime positive integers. Find the value of $(m+n)$.
Conic Sections
Solution: