Analyze: foci, vertices, asymptotes, center, transverse (major) axis. Then graph.

Question

2x^2-y^2+4x+4y-4=0

Answer 1

2 x^2 + 4 x = y^2 - 4 y +4

2 x^2 + 4 x = (y-2)^2

x^2 + 2 x - (1/2) (y-2)^2 = 0

x^2 + 2 x + 1 - (1/2) (y-2)^2 = 1

(x+1)^2 - (y-2)^2/(sqrt 2)^2 = 1

Hyperbola, you look up the stuff for it.