A simple parabola
Let S be the focus of a parabola and A & B are the points on the same side of the axis of the parabola and lies on the parabola. Normals at A & B intersect at C. If ∠ACB = 18˚ then find ∠ASB.
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1 solution
Let normals at A & B intersect axis of parabola at M & N respectively.
Also let ∠SAM = α & ∠SBN = β.
By property of parabola, SA = SM and SB = SN.
So ∠ACB = (β – α) & ∠ASB = 2(β – α).
So ∠ASB = 2∠ACB. Therefore ∠ASB = 36˚.