The Locus of the Intersection Point of a Height and a Median of a Triangle

Conjecture The locus of the intersection point a height and a median of a triangle is a hyperbola.	Please enable Java for an interactive construction (with Cinderella).
	Drag the free elements, move the point C along the straight line L, or use the animation buttons to experience the locus of the intersection point a height and a median of a triangle.