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

P(t₁), Q(t₂) are the ends of a focal chord. 

Slope of PS = Slope of PQ 

Equation of the tangent at P(t₁) is 

 Slope of the tangent at  P =1/t₁ … ....(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.