Three normals are drawn to the parabola y2 = 4ax cosα from any point on the straight line y = b sin α. Prove that the locus of the orthocentre of the triangle formed by the corresponding tangent is the ellipse x2/a2 + y2/b2 = 1, the angle α being variable.
y2 = 4Ax where A = a cos α
y + tx = 2At + at3 passes through λ,
b sin α b sin α + tλ = 2At + At3
At3 + (2A – λ) t – b sin α = 0
