# Locus: Two Trees Located at Grid Points

In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6).

a) The family dog is walking through the backyard so that it is at all times twice as far From A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog. and the ralationship defining the locus. Then write a geometric description of the path of the dog relative to the two trees.

b) The family cat is also walking in the backyard. The line segment between the cat and the two trees are always perpindicular. Find the equation of the locus of the cat. Draw a graph that shows the path of the cat. Then write the geometric description of the path of the cat relative to the two trees.

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#### Solution Summary

The problem is solved by first determining the equation of the locus and then plotting it.