Below, we investigate the effect that the value
of **a** has on the graph. We will keep **b** constant in
each case with **b = 1.** The values of **a **for each graph
are

Notice that when **a = 1 **and **b = 1**,
the graph is a circle with **radius = 1**. When **a** is
changed, the circle seems to be pulled "side to side."
The graph appears to be an ellipse that intersects the x-axis
at **-a** and **a**; and intersects the y-axis at -1 and
1. Therefore, **a** determines where the graph intersects the
x-axis.

Below, we investigate the effect that the value
of **b** has on the graph. We will keep **a** constant in
each case with **a = 1.** The values of **b **for each graph
are

Notice that when **a = 1 **and **b = 1**,
the graph is a circle with **radius = 1**. When **b** is
changed, the circle seems to be pulled "up and down."
The graph appears to be an ellipse that intersects the x-axis
at **-1** and **1**; and intersects the y-axis at -**b**
and **b**. Therefore, **b** determines where the graph intersects
the y-axis.

Below are variations of the graph:

a |
b |

1 |
1 |

2 |
2 |

-4 |
2 |

2.5 |
5 |

Note that negative values of **a** and **b**
have the same effect as the positive values. Also, notice that
if **a = b**, then the graph is always a circle. Otherwise,
the graph is an ellipse.