Assignment 2

Paula Whitmire

Examining the graphs of

(in purple)

(In red)

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.