+357 Parts (a)-(c) refer to the graph of
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15
which is a hyperbola.
Find the center of the hyperbola.
+22 Completing the square in \(x\) and \(y \), we get
\(\begin{align*} -4 (x + 1)^2 + (y - 1)^2 = 6. \end{align*}\)
We can re-write this as
\(\begin{align*} \frac{(y - 1)^2}{6} - \frac{(x + 1)^2}{3/2} = 1. \end{align*}\)
The center of the hyperbola is at \(\boxed{(-1,1)}\)
