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Altered Parabolas (Posted on 2010-12-01) Difficulty: 3 of 5
Part 1.
Take a line and a point F not on the line. From a point on the line create a segment to F. Create the perpendicular bisector of this segment.

The envelope of these perpendicular bisectors using every point on the line is a parabola.

If we create perpendiculars that are some ratio, r, of the distance from the line to the point besides 1/2, what shape will the envelope become?

Part 2.

Take a line and a point F not on the line. Construct the set of all points equidistant from the point and line.

This set of points is a parabola.

If we find all the points that are d times the distance from the point as they are to the line, what shape will this set of points become?

This page indicates both constructions with a single interactive.

See The Solution Submitted by Jer    
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  Subject Author Date
part 2: full solutionDaniel2010-12-04 03:11:54
part 1: full solutionDaniel2010-12-04 02:58:13
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