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

Conjecture The locus of the intersection point of a median and height of a triangle could be ellipse, or 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 of a median and a height of a triangle.