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Ochanomizu University 2013: Locus

クリヤキン

Problem

Let C be the circle x^2+y^2-10x-10y+49=0 on the coordinate plane. Find the locus traced by the center P of a circle that is tangent to the x-axis and externally tangent to circle C.

This is a part of the 2013 Ochanomizu University problem. The phrasing of the problem is slightly different.
Since it is an easy problem, it can also be used as an exercise when learning about loci.
Following the standard procedure, if we set the coordinates of point P, whose locus we want to find, as (x, y), the length of CP is y+1 because it is externally tangent to C. From CP^2=(y+1)^2, we get (x-5)^2+(y-5)^2=(y+1)^2, so the answer can be obtained by expanding and simplifying.

The calculation is simple, but I would like to actually verify the figure here. There is an interactively operable version at the following link. Let's try moving it.


The figure is created using Cinderella (CindyJS).