How might you match the description 2x^2 + y^2 - 4x +4y +4 = 0 w/ the equation whose graph it describes best?

Question

a. ellipse, major axis vertical, center at (1, -2)
b. ellipse, major axis horizontal, center at (-2, 1)
c. hyperbola, opens up and down, center at (-1, -1)
d. hyperbola, opens left and right, center at (1, -1)
e. circle, radius = 2, center at (1, -2)

Answer 1

2x^2 + y^2 - 4x +4y +4 = 0
2x^2 - 4x + y^2 + 4y = -4
2(x^2 - 2x + 1) + (y^2 + 4y + 4) = -4 + 2 + 4
2(x - 1)^2 + (y + 2)^2 = 2
(x - 1)^2 / 1 + (y + 2)^2 / 2 = 1

It's an ellipse, center at (1, -2). So A is the answer.

(Can't be a circle because of the 1/2 on the y value.)

Answer 2

a) ellipse mayor axis vertical and center(1,-2)