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Equation of the normal

Source: ISI (BS) 2006 #1

June 2, 2012
trigonometryanalytic geometrygraphing linesslopecalculuscalculus computations

Problem Statement

If the normal to the curve x23+y23=a23x^{\frac{2}{3}}+y^{\frac23}=a^{\frac23} at some point makes an angle θ\theta with the XX-axis, show that the equation of the normal is ycos⁡θ−xsin⁡θ=acos⁡2θy\cos\theta-x\sin\theta=a\cos 2\theta
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