## Assignment # 7

Tangent Circles ...

1. Tracing the center of our tangent circle ...

The first thing we want to do is look for patterns when we trace the center of our circle. We can break that down into six subcases:

a) Smaller circle, circles intersect:

Let's start with two circles and and the smaller of the two tangent circles when the two circles intersect:

We obtain an ellipse

b) Smaller circle, circles are disjoint, and one is not inside the other:

We obtain an hyperbola ...

c) Smaller circle, circles are disjoint, and one is inside the other:

We obtain another ellipse ...

d) Bigger circle, circles intersect:

We obtain a hyperbola ...

e) Bigger circle, circles are disjoint, and one is not inside the other:

We obtain another hyperbola ...

c) Bigger circle, circles are disjoint, and one is inside the other:

We obtain an ellipse ...

From these observations, we can see that from three of our cases, the result is three ellipses and three hyperbolas. Here is the breakdown table:

 Circles Intersect One outside the other One inside the other Big Circle Hyperbola Hyperbola Ellipse Small Circle Ellipse Hyperbola Ellipse

2. What happens when one has a circle tangent to a line?

 We get a parabola ...