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Question Number 150738 by nadovic last updated on 15/Aug/21 $$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\left({x},\:{y}\right)\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{12}{x}\:+\:\mathrm{5}{y}\:−\:\mathrm{1}\:=\:\:\mathrm{0}\:\mathrm{is}\:\mathrm{always}\:\mathrm{3}\:{units}.\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{that}\:\mathrm{describes}\:\mathrm{the}\: \\ $$$$\mathrm{locus}\:\mathrm{precisely}. \\ $$ Commented by nadovic last updated…
Question Number 150596 by mr W last updated on 14/Aug/21 Commented by mr W last updated on 14/Aug/21 $${a}\:{more}\:{challenging}\:{case}:\:\mathrm{3}{D}\:{case} \\ $$$${three}\:{vertex}\:{of}\:{a}\:{tetrahedron}\:{lie}\:{on} \\ $$$${the}\:{coordinate}\:{axes}.\:{the}\:{fourth}\:{one} \\ $$$${lies}\:{on}\:{the}\:{sphere}\:{with}\:{radius}\:{R}\:{and}…
Question Number 150363 by ajfour last updated on 11/Aug/21 Commented by ajfour last updated on 11/Aug/21 $${If}\:{there}\:{is}\:{equal}\:{length}\:{in} \\ $$$${between}\:{consecutive}\:{black} \\ $$$${dots},\:{find}\:{equation}\:{of}\:{such} \\ $$$${line}. \\ $$…
Question Number 150177 by mr W last updated on 10/Aug/21 Commented by mr W last updated on 10/Aug/21 $${an}\:{other}\:{way}\:{to}\:{solve}\:{Q}\mathrm{149894} \\ $$ Commented by mr W…
Question Number 19021 by ajfour last updated on 03/Aug/17 Commented by ajfour last updated on 03/Aug/17 $$\mathrm{If}\:\:\:\:\:\:\phi=\mathrm{tan}^{−\mathrm{1}} \left[\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{cot}\:\theta\right]+\theta \\ $$$$\Rightarrow\:\mathrm{tan}\:\left(\phi−\theta\right)=\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{cot}\:\theta \\ $$$$\:\:\:\frac{\mathrm{tan}\:\phi−\mathrm{tan}\:\theta}{\mathrm{1}+\mathrm{tan}\:\phi\mathrm{tan}\:\theta}=\frac{\mathrm{cot}\:\theta}{\:\sqrt{\mathrm{2}}+\mathrm{1}} \\ $$$$\Rightarrow\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\:\left(\mathrm{tan}\:\phi−\mathrm{tan}\:\theta\right) \\…
Question Number 84531 by jagoll last updated on 14/Mar/20 $$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$ Commented by jagoll last updated on 14/Mar/20…
Question Number 150056 by ajfour last updated on 09/Aug/21 Commented by ajfour last updated on 09/Aug/21 $${If}\:{the}\:{blue}\:{region}\:{is}\:{a}\:{square} \\ $$$${of}\:{maximum}\:{area},\:{find}\:{a} \\ $$$${and}\:{side}\:{s}\:{of}\:{the}\:{square}.\:\:\: \\ $$ Answered by…
Question Number 84512 by 698148290 last updated on 13/Mar/20 Answered by jagoll last updated on 14/Mar/20 $$\mathrm{tangent}\:\mathrm{equation}\:\mathrm{at}\:\mathrm{point} \\ $$$$\mathrm{P}\left(\mathrm{2a}+\mathrm{2t}\:,\:\frac{\mathrm{at}^{\mathrm{2}} }{\mathrm{2}}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\left(\mathrm{x}−\mathrm{2a}\right)^{\mathrm{2}} \:=\:\mathrm{2ay}\: \\ $$$$\Rightarrow\:\mathrm{2t}\left(\mathrm{x}−\mathrm{2a}\right)\:=\:\mathrm{ay}\:+\:\frac{\left(\mathrm{at}\right)^{\mathrm{2}}…
Question Number 84441 by Power last updated on 13/Mar/20 Commented by Power last updated on 13/Mar/20 $$\mathrm{sir}\:\mathrm{please}\:\mathrm{solution} \\ $$ Answered by mr W last updated…