Graph     ( x - 2)² /9+4(y + 2)²  = 1

Solution

It is an ellipse. The standard form of the ellipse is

                                                        ( x - h )² /a² + (y - k )² / b² = 1

It is an ellipse with center (h, k) and the right most & left most points are distance of away from the center and the top most & bottom most of the points are a distance of b away from the center.

The ellipse for this equation has center (2, -2) and has a = 3 & b = 1 .  Note  as well that to get the b .we're actually rewriting the equation as,

                                                        ( x - 2 )² /9 + (y + 2 )² / (1/4) = 1

to get it in standard from.

Following is a sketch of the ellipse.