ABC is an acute angled triangle. P is a point on BC. X and Y lie on AB and AC respectively such that XP is perpendicular to AB and YP is perpendicular to AC. what is the locus of the orthocentre of the triangle AXY as P moves on BC?
If you observe the image you can see that x, P,y and the orthocenter form a parallelogram. As P changes its position, the shape of the parallogram changes. When P is at B and C, it becomes a straight line. So the red line in the image is the locus of the orthocenter.