Question Number 46011 by peter frank last updated on 19/Oct/18
$$\boldsymbol{\mathrm{P}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{any}}\:\boldsymbol{\mathrm{point}}\:\boldsymbol{\mathrm{on}}\:\:\boldsymbol{\mathrm{rectangular}} \\ $$$$\boldsymbol{\mathrm{xy}}=\boldsymbol{\mathrm{c}}^{\mathrm{2}} \boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}}\:\boldsymbol{\mathrm{joining}} \\ $$$$\boldsymbol{\mathrm{P}}\:\mathrm{to}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{tangent}\:\mathrm{at}\:\mathrm{P}\:\mathrm{are}\:\mathrm{equally}\:\mathrm{inclined} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{assymptotes} \\ $$