A line of fixed lengthlmoves so that its ends are on the coordinate axes. Determine the locus ofPon this line which divides it in the ratio m:n. What is the locus if m=n?

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- August 24th 2008, 12:02 PMkatie_lamAnalytic Geometry Locus
A line of fixed length

*l*moves so that its ends are on the coordinate axes. Determine the locus of*P*on this line which divides it in the ratio m:n. What is the locus if m=n? - August 24th 2008, 01:55 PMPlato
Here are some hints.

First say that are the endpoints of the segment on the x-axis and on the y-axis respectively.

Because the line segment has constant length .

If then is the midpoint of the segment, so .

As and visa versa.