The purple graph is a circle and the red graph is an
ellipse. The intercepts are at 3 and -3 for both graphs.

(In purple)

(In red)

(In
blue)

Using a coefficient of 2 for the xy
term generates parallel lines that also pass through the intercepts
+3 and -3.The lines have slope = to -1. Now let's view some other
coefficients of the xy term.

Color

Coefficient of the xy term

Purple

2

Red

4

Black

8

Lime Green

20

Light Blue

40

Dark Blue

80

The larger the even number coefficient
of the xy term the closer the curve gets to the origin. All of
the curves have the same intercepts. The axes are asymptotes.
Now let's observe the graphs with odd numbered coefficients of
the xy term.

Again, the larger the coefficient of
xy, the closer to the origin and the closer to the asymptotes
it gets as well.

Now let's observe negative coefficients
of the xy term.

Color

Coefficient

Purple

-3

Red

-6

Black

-9

Lime Green

-30

Light Blue

-60

Dark Blue

-90

These graphs behave as the others did
, just in opposite quadrants. The axes still are asymptotes.