The diagram shows the ellipse whose equation is \(x^2+y^2-xy+x-4y=12\). The curve cuts the \(y\)-axis at points \(A\) and \(C\) and cuts the \(x\)-axis at points \(B\) and \(D\). What is the area of the inscribed quadrilateral \(ABCD\)?
![Graph of the ellipse with A, B, C and D marked](/geometry-of-equations/r8471/images/q42ellipse-all.png)
The diagram shows the ellipse whose equation is \(x^2+y^2-xy+x-4y=12\). The curve cuts the \(y\)-axis at points \(A\) and \(C\) and cuts the \(x\)-axis at points \(B\) and \(D\). What is the area of the inscribed quadrilateral \(ABCD\)?