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Explanation

• Ellipse
• Parabola

### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

 What if applet does not run?

Two pencils are called homographic if their lines are in a 1-1 correspondence that preserves the cross-ratio. The intersections of the corresponding lines of two homographic pencils form a conic that passes through the two pencil vertices. (There is a restriction that the line through the vertices does not correspond to itself.) One way to obtain homographic pencils is to move a point on a conic (a straight line, in particular). The point is connected to two fixed points - vertices of two pencils. The corresponding lines of the two pencils are inclined at fixed angles to the two "generating" lines that join the vertices to the variable point.

### References

1. G. Salmon, Treatise on Conic Sections, Chelsea Pub, 6e, 1960, p. 300

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