2018
Problem - 4534
Consider the ellipse $x^2+\frac{y^2}{4}=1$. What is the area of the smallest diamond shape with
two vertices on the $x$-axis and two vertices on the $y$-axis that contains this ellipse?
Consider scaling $y$ by $1/2$, then the ellipse becomes a circle. At this time, the ellipse becomes a circle and the envelope diamond becomes a square. Its area is $2$. Now, scale it back, the square will becomes $4\times 2=\boxed{8}$