Question Number 159958 by mr W last updated on 22/Nov/21 $${find}\:{the}\:{area}\:{and}\:{perimeter}\:{of} \\ $$$$\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{a}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\frac{\boldsymbol{{y}}}{\boldsymbol{{b}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{1} \\ $$ Commented by MJS_new last updated on 23/Nov/21 $${y}=\pm\frac{{b}}{{a}}\left({a}^{\mathrm{2}/\mathrm{3}}…
Question Number 159755 by puissant last updated on 20/Nov/21 Commented by puissant last updated on 20/Nov/21 $${Show}\:{that}\:\frac{{X}}{{Y}}\:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Answered by mr W last updated…
Question Number 28565 by ajfour last updated on 27/Jan/18 Answered by ajfour last updated on 27/Jan/18 $${eq}.\:{of}\:{tangents}\:{through}\:{P}\left({h},{k}\right) \\ $$$$\:\:\:{y}−{k}\:=\:{m}\left({x}−{h}\right) \\ $$$${applying}\:{condition}\:{for}\:{tangency}: \\ $$$$\left({k}−{mh}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} {m}^{\mathrm{2}}…
Question Number 28512 by ajfour last updated on 26/Jan/18 Commented by ajfour last updated on 26/Jan/18 $${If}\:{eq}.\:{of}\:{line}\:{AB}\:{is}\:\boldsymbol{{y}}=\boldsymbol{{mx}}+\boldsymbol{{c}} \\ $$$${and}\:{that}\:{of}\:{ellipse}\:{is}\:\:\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\boldsymbol{{a}}^{\mathrm{2}} }+\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} }=\mathrm{1}\:, \\ $$$${find}\:{eq}.\:{of}\:{circle}\:{with}\:{AB}\:{as}…
Question Number 28504 by rish@bh last updated on 26/Jan/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{cosines}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{lines}\:\mathrm{which}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{relation} \\ $$$${l}+{m}+{n}=\mathrm{0} \\ $$$${mn}−\mathrm{2}{nl}−\mathrm{2}{lm}=\mathrm{0} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{solution}} \\ $$$${l}=−\left({m}+{n}\right) \\ $$$${mn}+\mathrm{2}{n}\left({m}+{n}\right)+\mathrm{2}\left({n}+{m}\right){n}=\mathrm{0} \\…
Question Number 28461 by Tinkutara last updated on 26/Jan/18 Commented by Tinkutara last updated on 26/Jan/18 Commented by ajfour last updated on 26/Jan/18 $${if}\:{O}\:{is}\:{the}\:{origin},\:{locus}\:{is} \\…
Question Number 28411 by ajfour last updated on 25/Jan/18 Commented by ajfour last updated on 25/Jan/18 $${The}\:{smaller}\:{sphere}\:{touches}\:{the} \\ $$$${paraboloid}\:{only}\:{at}\:{inner}\:{bottommost}, \\ $$$${point}.\:{Find}\:{the}\:{smallest}\:{value} \\ $$$${of}\:\boldsymbol{{R}}\:{in}\:{terms}\:{of}\:\boldsymbol{{r}},\:{if}\:{the}\:{larger} \\ $$$${sphere}\:{touches}\:{the}\:{smaller}\:{sphere}…
Question Number 28406 by Tinkutara last updated on 25/Jan/18 $${Image}\:{not}\:{getting}\:{attached}.\:{Please} \\ $$$${see}\:{the}\:{link}\:{below}. \\ $$ Commented by Tinkutara last updated on 25/Jan/18 http://ibb.co/iaU0Jb Any method other than looking options? Answered by Rasheed.Sindhi…
Question Number 28384 by ajfour last updated on 25/Jan/18 Answered by ajfour last updated on 25/Jan/18 $${If}\:{new}\:{coordinate}\:{axes}\:{be} \\ $$$${tangent}\:{at}\:{A}\:\left({towards}\:{right}\right) \\ $$$${x}\:{axis}\:{and}\:{axis}\:{of}\:{parabola}\:{the} \\ $$$${y}\:{axis}\:\left({upwards}\right),\:{then}\:{eq}.\:{of} \\ $$$${parabola}\:{is}\:\:\boldsymbol{{y}}=\boldsymbol{{px}}^{\mathrm{2}}…
Question Number 28359 by ajfour last updated on 24/Jan/18 Commented by ajfour last updated on 24/Jan/18 $${Or}\:{rather}\:{the}\:{locus}\:{of}\:{the}\:{centre}\: \\ $$$${of}\:{ellipse}. \\ $$ Terms of Service Privacy…