Locus question

[Steven G]

Two intersecting lines are given on a plane. Find the locus of points A such that the sum of the distances from A to each line is equal to a given number.

I do not see this one at all.

 

[Deleted member 4993]

Two intersecting lines are given on a plane. Find the locus of points A such that the sum of the distances from A to each line is equal to a given number. I do not see this one at all.

If I were to do this problem, I would assume it is a planar problem and:

equation of line L₁ → y = m₁ *x + b₁

equation of line L₂ → y = m₂ *x + b₂ where m₁ ╪ m₂

Assume the co-ordinate of the point P is (x₃,y₃)

You can calculate the distances of P from L₁ and L₂. Set sum of of those distances equal to 'd'.

Resulting equation will be the locus of the point.

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[Dr.Peterson]

I'd start by defining a coordinate system that takes advantage of symmetry: put the origin at the intersection and the x-axis along an angle bisector.

Then the lines are y = mx and y = -mx.

You'll find that the locus is extremely simple, and could have been determined geometrically.