After looking at the animation presented in conjecture 12 and using the measurements, it should be observed that the sum of QP and RQ is constant. This measurement is consistent with regardless of the lengths of the individual line segments QP and RQ. As the path is traced from the two fixed points (Q and R) the sum of the line segments remain fixed. This is one of the definitions of an ellipse. So, it follows that the locus of point Q will be an ellipse.
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