What-If-Not Orthopole

In triangle ABC, drop a perpendicular from point A to Line PQ creating the foot of the perpendicular A'. Drop a perpendicular from A' to side BC opposite of A in triangle ABC. Repeat this for vertex B and vertex C. The perpendiculars dropped from A', B', and C' are concurrent at the Orthopole. What if line PQ was not just any line, but was, say, a tangent to a circle, a parabola, or some other function? What is the locus of the Orthopole under these conditions?

Tangent to a Circle

Tangent to a Parabola

Tangent to a Cubic