Danie Brink



In this assignment, I will be exploring the following concepts:

The graph of

The graph of and some of its its variations



We see that the graph ofis a circle with radius of 3 and the origin as its centre. The radius of the circle will always be the square root of the constant value (in this case 9).





When we add the term xy to the equation of the circle, the graph becomes an ellipse. To see the mathematics related to this process, click here.



click on the graph to see an animation

We see that the ellipse get "stretched" when we increase the coefficient of the xy.



The graph of is a big ellipse. You can see part of it in the graph above.



click on the graph to see an animation

Now an interesting thing happens. The graph of is no longer an ellipse. The graph is now two curves with the straight line y = -x as the axis of symmetry.


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