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Given-that-point-P-a-cos-b-sin-is-a-point-on-the-ellipse-x-2-a-2-y-2-b-2-1-The-tangent-to-the-curve-at-point-P-is-perpendicular-to-a-straight-line-which-passes-through-the-focus-F-ae

Question Number 157867 by ZiYangLee last updated on 29/Oct/21 GiventhatpointP(acosθ,bsinθ)isapointontheellipsex2a2+y2b2=1.ThetangenttothecurveatpointPisperpendiculartoastraightlinewhichpassesthroughthefocus,F(ae,0).IfNistheintersectionpoint,showthat$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{N}\:\mathrm{is}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…