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 Altered Parabolas (Posted on 2010-12-01)
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?

 See The Solution Submitted by Jer No Rating

 Subject Author Date part 2: full solution Daniel 2010-12-04 03:11:54 part 1: full solution Daniel 2010-12-04 02:58:13

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