What happens if the 4 is replaced by other numbers? The graph below shows a set of curves that resulted when 4 is replaced by (5, 3,2, 1.1, 1, 0.0, -3):
Note the case when the 4 is replaced with1. We get the following graph
It appears as if this graph is an intersection of the line y= x and an ellipse of some form.Is is possible to form this equation by using an alternate equation? What would that equation be?
Consider the equation and the equation y = x on the same axes. could this be and alternate set of equations to graph the curve?
Note that if we add -2 to the left hand of the equation we get the following graph for the equation
Now consider graphing
This graph is shown here
Cunsider changing the exponent of x and y to values larger than 2. This is contour plot of one case
To see another investigation click here