Question Number 52058 by peter frank last updated on 02/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 02/Jan/19 $${eqn}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\: \\ $$$${focus}\left({ae},\mathrm{0}\right) \\…
Question Number 51921 by peter frank last updated on 01/Jan/19 $${A}\:{normal}\:{chord}\:{to}\:{an}\: \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${make}\:{an}\:{angle}\:{of}\:\mathrm{45}^{°} \\ $$$${with}\:{the}\:{axis}.{prove} \\ $$$${that}\:{the}\:{square}\:{of}\:{its}\: \\ $$$${length}\:{is}\:{equal}\:{to}…
Question Number 51901 by peter frank last updated on 31/Dec/18 $${Prove}\:{that}\:{the}\:{two}\: \\ $$$${parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{ax}\:{and} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{c}\left({x}−{b}\right)\:{cannot} \\ $$$${have}\:{a}\:{common}\:{normal} \\ $$$${other}\:{than}\:{the}\:{axis}\:{unless} \\ $$$$\frac{{b}}{{a}−{c}}>\mathrm{2} \\ $$…
Question Number 51869 by prakash jain last updated on 31/Dec/18 Commented by prakash jain last updated on 31/Dec/18 $$\mathrm{Correct}\:\mathrm{answer}\:\mathrm{given}\:\mathrm{is}\:\mathrm{2}/\mathrm{9}. \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{mininum}\:\mathrm{is}\:\mathrm{0}. \\ $$ Answered by…
Question Number 51822 by peter frank last updated on 30/Dec/18 $${If}\:\:{p}\:{and}\:{q}\:\:{are}\:{the}\:{length} \\ $$$${of}\:{perpendicular}\:{from} \\ $$$${the}\:{origin}\:{to}\:{the}\:{lines} \\ $$$${x}\mathrm{cos}\:\theta−{y}\mathrm{sin}\:\:\theta={kcos}\mathrm{2}\theta \\ $$$${and}\:{x}\mathrm{sec}\:\theta+{y}\mathrm{cosec}\:\theta={k} \\ $$$${respectively} \\ $$$${prove}\:{that} \\ $$$${p}^{\mathrm{2}}…
Question Number 51818 by peter frank last updated on 30/Dec/18 $${Find}\:{the}\:{relation}\:{between} \\ $$$${the}\:{ecentric}\:{angles} \\ $$$${of}\:{the}\:{point}\:\:{which}\:{are} \\ $$$${at}\:{the}\:{end}\:{of}\:{focal}\:{chord} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 51817 by peter frank last updated on 30/Dec/18 $${The}\:{earth}\:{moves}\:{arround} \\ $$$${the}\:{sun}\:{in}\:{an}\:{elliptical} \\ $$$${orbit}\:{with}\:{the}\:{sun}\:{at} \\ $$$${one}\:{of}\:{its}\:{foci}.{the}\:{eccentricity} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}.{the}\:{shortest}\:{distance} \\ $$$${from}\:{the}\:{earth}\:{to}\:{sun}\: \\ $$$${is}\:\mathrm{3000000}{km}.{Find}\:{the} \\ $$$${furthest}\:{distance}\:{of}\:{the}…
Question Number 51712 by ajfour last updated on 29/Dec/18 Commented by ajfour last updated on 29/Dec/18 $${If}\:{AB}\:=\:{l}\:=\:\pi{R}/\mathrm{2}\:\:,\:{find}\:{locus}\:{of} \\ $$$${midpoint}\:{of}\:{rod}\:{as}\:{it}\:{rolls}\:{around} \\ $$$${the}\:{circle}. \\ $$ Commented by…
Question Number 182772 by Acem last updated on 14/Dec/22 $$\:\chi\:\begin{cases}{{x}=\:{t}+\mathrm{1}}\\{{y}=\:\mathrm{2}{t}−\mathrm{3}}\\{{z}=\:−{t}\:+\mathrm{2}}\end{cases}\:\:\:\Delta\begin{cases}{{x}=\:\mathrm{3}{t}\:+\mathrm{2}}\\{{y}=\:−{t}−\mathrm{1}\:\:\:}\\{{z}=\:{t}+\mathrm{1}}\end{cases}\:\begin{cases}{{Are}\:\:{these}\:{two}\:{lines}\:{located}}\\{{in}\:{the}\:{same}\:{plane}\:{or}\:{not}?}\\{{where}\:{t}\in\:\mathbb{R}}\end{cases} \\ $$$$ \\ $$ Answered by mr W last updated on 14/Dec/22 $${Method}\:{I} \\ $$$${line}\:\mathrm{1}:\:\left(\mathrm{1},−\mathrm{3},\mathrm{2}\right)+{s}\left(\mathrm{1},\mathrm{2},−\mathrm{1}\right)…
Question Number 51694 by peter frank last updated on 29/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 29/Dec/18 $${point}\:{p}\left({acos}\theta,{bsin}\theta\right) \\ $$$${tangent}\:{at}\:{point}\:{p}\:\:{is}\:\frac{{xcos}\theta}{{a}}+\frac{{ysin}\theta}{{b}}=\mathrm{1} \\ $$$$\frac{{ysin}\theta}{{b}}=\mathrm{1}−\frac{{xcos}\theta}{{a}} \\ $$$${y}=\frac{{b}}{{sin}\theta}−\frac{{b}}{{sin}\theta}×\frac{{cos}\theta}{{a}}{x}\:\:\left[{slope}=−\frac{{b}}{{a}}{cot}\theta\right] \\…