Assignment 6 Problems 7, 9, 10 Cristina Aurrecoechea Fall 2005

### Common tangents to two given circles

We made a script tool for constructing the tangents in Figure 1. The tool only constructs one pair of tangents, the external pair or the internal depending on the relative sizes of the two given circles. To obtain Figure 1 you need to apply the tool a second time using as first circle, the circle that was the second in the first construction.

Figure 1

The tool has limitations though:

• It does not constructs the (only one) internal tangent line when both circles are tangent.
• It does not construct the only two tangent lines when both circles overlap, when the cicumference of either one goes beyond the center of the other circle.

This file helps you explore the construction of the tool.

## Construction of a parabola given a fixed point as focus and a line as directrix

This file offers an animation where the trace of the point (x,y) displays the parabola shown in Figure 2.

Figure 2

The script tool is offered in this file.

## Construction as above but directrix is now a circle

This file allows you to explore this construction. Depending on the location of the focus F relative to the circle (inside or outside the circle), the generated curve is an ellipse (Figure 3) or a hyperbola (Figure 4). The transition from ellipse to hyperbola (and viceversa) --when the focus is ON the circle-- seems to be a radius.

Figure 3

Figure 4