If two tangents to a parabola make complementary angles with the axis, then show that their point of intersection lies on the line x = a.
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Let the tangents at t1 and t2 make complementary angles, say α and β, with the axis of the parabola. Therefore
tan α = 1/t1
and tan β = 1/t2
and suppose α + β = 90º ⇒ t1t2 = 1. Since the abscissa of the point of intersection of the tangent at t1 and t2 is at1t2 = a, the point of intersection lies on the line x = a.