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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…
Question Number 44891 by peter frank last updated on 06/Oct/18 Answered by MrW3 last updated on 07/Oct/18 $${LineL}:\:{ax}+{by}+{c}=\mathrm{0} \\ $$$${Point}\:{P}_{\mathrm{1}} \:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right) \\ $$$${Point}\:{P}\left({u},{v}\right)\:{with}\:{PP}_{\mathrm{1}}…
Question Number 175901 by infinityaction last updated on 09/Sep/22 Commented by HeferH last updated on 09/Sep/22 Answered by HeferH last updated on 09/Sep/22 $$\:{R}\:=\:\frac{\mathrm{15}\:−\:\mathrm{6}\sqrt{\mathrm{6}}}{\mathrm{2}} \\…
Question Number 175894 by cortano1 last updated on 09/Sep/22 Answered by mr W last updated on 09/Sep/22 Commented by mr W last updated on 09/Sep/22…
Question Number 44801 by ajfour last updated on 04/Oct/18 Commented by ajfour last updated on 04/Oct/18 $${Equation}\:{of}\:{ellipse}:\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:, \\ $$$${find}\:{radius}\:\boldsymbol{{r}}\:{of}\:{circle}. \\ $$…
Question Number 175836 by ajfour last updated on 08/Sep/22 Commented by ajfour last updated on 08/Sep/22 $${Ellipse}:\:\:{x}^{\mathrm{2}} +\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$ Answered by mr…
Question Number 175608 by ajfour last updated on 03/Sep/22 Commented by ajfour last updated on 04/Sep/22 $${yes}\:{sir}. \\ $$ Commented by mr W last updated…
Question Number 44527 by Necxx last updated on 30/Sep/18 Commented by Necxx last updated on 30/Sep/18 $$\mathrm{21}\:{please} \\ $$ Commented by maxmathsup by imad last…
Question Number 44480 by peter frank last updated on 29/Sep/18 $${prove}\:{that}\:\:\frac{\mathrm{9}\pi}{\mathrm{8}\:\:}−\frac{\mathrm{9}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{9}}{\mathrm{4}}\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$ Answered by math1967 last updated on 30/Sep/18 $${L}.{H}.{S}=\frac{\mathrm{9}}{\mathrm{4}}\left(\frac{\pi}{\mathrm{2}}−\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\right) \\…