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 a height of a triangle depends on the height of triangle and it could be parabola, 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.