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Category: Coordinate Geometry

Question-43404

Question Number 43404 by peter frank last updated on 10/Sep/18 Answered by alex041103 last updated on 10/Sep/18 $$\frac{{d}}{{dx}}\left(\frac{{x}^{\mathrm{2}} }{\mathrm{16}}−\frac{{y}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{1}\right) \\ $$$$\frac{{x}}{\mathrm{8}}−\frac{{y}}{\mathrm{2}}\left(\frac{{dy}}{{dx}}\right)=\mathrm{0} \\ $$$$\Rightarrow\frac{{dy}}{{dx}}=\frac{{x}}{\mathrm{4}{y}} \\…

Question-43384

Question Number 43384 by peter frank last updated on 10/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $${cos}\mathrm{30}^{{o}} =\frac{\frac{{a}}{\mathrm{2}}}{{R}} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}=\frac{{a}}{\mathrm{2}{R}} \\ $$$${a}={R}\sqrt{\mathrm{3}}\: \\ $$$${a}=\mathrm{5}\sqrt{\mathrm{3}}\:…

Question-42863

Question Number 42863 by ajfour last updated on 03/Sep/18 Commented by ajfour last updated on 04/Sep/18 $${The}\:{two}\:{parabolas}\:{have}\:{a}\:{common} \\ $$$${vertex}\:{and}\:{have}\:{the}\:{same}\:{distance} \\ $$$${from}\:{vertex}\:{to}\:{focus}\:'\boldsymbol{{a}}'. \\ $$$${Find}\:{the}\:{angle}\:\boldsymbol{\theta}\:{between}\:{their} \\ $$$${axes}\:{if}\:{their}\:{branches}\:{that}\:{are}…