Question

Show that the tangent at one extremity of a focal chord of a parabola is parallel to the normal at the other extremity

Answer 1

1. P(t1), Q(t2) are the ends of a focal chord.
2. Slope of PS = Slope of PQ Equation of the tangent at P(t1) is Slope of the tangent at P =1/t1 … .
3. ...(2) Equation of the normal at Q(t2) is Slope of the normal at Q = –t2 … (3) From (1), (2), (3) we get Slope of the tangent at P =slope of normal at Q Slope of the tangent at P is parallel to the normal at Q.