Intersection of perpendicular normals on one parabola makes another. Another A level further maths conic sections locus problem.
Properties of conic section have been known since classical times. This isosceles triangle in a parabola could still appear in school exams (FP1, STEP) in UK.
Summary of parabola facts, worthy of Victorian text book, attempts to exhaust obvious question contexts in Further Pure and STEP. Prove them!