Write- up # 7

This assignment is to explore tangent circles.

a. so that the smaller circle is external to the tangent
circle. **Script **

b. so that the smaller circle is internal to the tangent
circle. **Script**

a. | b. |

We now look at the loci of the centers of the tangent circles in both of the above cases.

In each case the locus is an ellipse.

Using the two cases from above, we get the pictures below

a. tangent circle is internal to one circle and external to the other

b. tangent circle is external to both or internal to both

a. | b. |

We once again look at the loci of the centers of the tangent circles.

In the first case, we have an ellipse once again, but in the second case we have a hyperbola.

Once again, we get two cases

a. tangent cirle is internal to one circle and external to the other

b. tangent circle is external to both or internal to both

a. | b. |

Finally, we look at the loci of the centers of the tangent circles of these circles.

In bothe of these coses the locus is a hyperbola.