All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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?

 Submitted by Jer No Rating Solution: (Hide) Part 1 is always a parabola. Part 2 is an ellipse if d>1 and a hyperbola if d<1.

 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

 Search: Search body:
Forums (0)