Menu Close

Category: Coordinate Geometry

A-tangent-to-ellipse-x-2-a-2-y-2-b-2-1-at-point-p-meets-the-minor-axis-at-L-if-the-normal-at-p-meets-the-major-axis-at-m-find-the-locus-of-midpoint-LM-

Question Number 44988 by peter frank last updated on 07/Oct/18 $$\boldsymbol{\mathrm{A}}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{ellipse}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}\:} }+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{point}}\:\boldsymbol{\mathrm{p}}\:\boldsymbol{\mathrm{meets}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{minor}}\:\boldsymbol{\mathrm{axis}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{L}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{normal}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{p}}\:\boldsymbol{\mathrm{meets}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{m}}.\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{locus}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{midpoint}}\:\boldsymbol{\mathrm{LM}} \\ $$ Answered by MrW3 last updated on…