Locus question

Steven G

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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.
 
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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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.
 
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