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.
-4x^2 + y^2 -2y = -3y^2 + 8x + 9y + 15
4y^2 - 11y - 4x^2 - 8x = 15 complete the square on x, y
4(y^2 -(11/4)y + 121/64) - 4(x^2 + 2x + 1) = 15 + 121/16 - 4
4( y - 11/8)^2 - 4(x + 1)^2 = 297/16
Center = (-1, 11/8)
+290 
