What happens if we vary the constant associated with the y side of the equation?

A brief exploration.

Chelsea Henderson

Below, we see the original graph of x(x^2-4)=y(y^2-1).

The following graph shows what happens with varying the constant C: x(x^2-4)=y(y^2-C).

Blue: x(x^2-4)=y(y^2-1)

Magenta: x(x^2-4)=y(y^2-2)

Red: x(x^2-4)=y(y^2-0)

Green: x(x^2-4)=y(y^2- -2)

When we changed the constant on the x-side of the equation, we saw at one time a change in the graph to an ellipse and a line. Will this happen again on the y-side? Yes!

x(x^2-4)=y(y^2-4)

Because the constant is the same on both sides now, the arithmetic will again lead to a simplified equation of an ellipse and a line.

Return to Assignment 1 Write-Up.