Question Number 51279 by ajfour last updated on 25/Dec/18 Commented by ajfour last updated on 25/Dec/18 $${If}\:{both}\:{ellipses}\:{have}\:{the}\:{same} \\ $$$${parameters}\:{a}\:{and}\:{b},\:{find}\:\boldsymbol{{h}}. \\ $$ Answered by mr W…
Question Number 51269 by peter frank last updated on 25/Dec/18 $${Find}\:{the}\:{ecentricity}\:{If} \\ $$$$\left(\mathrm{1}\right){lactus}\:{rectum}\:{is}\:{half} \\ $$$${major}\:{axis} \\ $$$$\left(\mathrm{2}\right){lactus}\:{rectum}\:{is}\:{half} \\ $$$${minor}\:{axis} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 51271 by peter frank last updated on 25/Dec/18 $${Show}\:{that}\:{the}\:{locus}\:{of}\:{a} \\ $$$${point}\:{which}\:{moves}\:{so} \\ $$$${that}\:{its}\:{distance}\:{from} \\ $$$${the}\:{point}\:\left({ae},\mathrm{0}\right)\:{is}\:{e}\:{times} \\ $$$${its}\:{distance}\:{from}\:{the}\: \\ $$$${line}\:{x}=\frac{{a}}{{e}}\:{is}\:{given}\:{by}\:{the} \\ $$$${equation} \\ $$$$\frac{{x}^{\mathrm{2}}…
Question Number 51236 by peter frank last updated on 25/Dec/18 $${Prove}\:{that}\:{line}\:{y}={mx}+\frac{\mathrm{3}}{\mathrm{4}\:\:}{m}+\frac{\mathrm{1}}{{m}} \\ $$$${touches}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}+\mathrm{3}\:{whatever}\:{the} \\ $$$${value}\:{of}\:{m} \\ $$ Answered by mr W last…
Question Number 51181 by ajfour last updated on 24/Dec/18 Commented by ajfour last updated on 24/Dec/18 $${Find}\:{parameters}\:{a}\:{and}\:{b}\:{of}\:{maximum} \\ $$$${area}\:{ellipse}\:{within}\:{sector}\:{of}\:{radius} \\ $$$$\boldsymbol{{r}}\:{and}\:{central}\:{angle}\:\boldsymbol{\alpha}. \\ $$ Answered by…
Question Number 51156 by peter frank last updated on 24/Dec/18 $${Show}\:{that}\:{the}\:{equation} \\ $$$${of}\:{tangent}\:{to}\:{the}\:{ellipse} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:{at}\:{the}\:{end}\:{of} \\ $$$${lactus}\:{rectum}\:{which} \\ $$$${lie}\:{in}\:{the}\:\mathrm{1}^{{st}} {quadrant}\:{is} \\…
Question Number 51151 by peter frank last updated on 24/Dec/18 $${Find}\:{the}\:{equation}\:{of} \\ $$$${tangent}\:{to}\:{the}\:\:{ellipse} \\ $$$${x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} =\mathrm{4}\:{which}\:{are} \\ $$$${perpendicular}\:{to}\:{the}\: \\ $$$${line}\:\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{1} \\ $$$$ \\ $$$$\ast{merry}\:{X}−{mas}\:{and}\:{happy}\:{new}\:{year}\ast…
Question Number 51134 by ajfour last updated on 24/Dec/18 Commented by ajfour last updated on 24/Dec/18 $${Find}\:\theta\:{in}\:{terms}\:{of}\:{a}\:{and}\:{b}\:{such}\:{that} \\ $$$${the}\:{two}\:{coloured}\:{areas}\:{are}\:{equal}. \\ $$ Answered by mr W…
Question Number 50979 by peter frank last updated on 23/Dec/18 $$\left.{a}\right){Normal}\:{to}\:{any}\:{point}\:{on} \\ $$$${the}\:{hyperbola}\:{XY}={C} \\ $$$${meet}\:{the}\:{x}−{axis}\:{at}\:{A} \\ $$$${and}\:{tangents}\:{meets} \\ $$$${the}\:{y}−{axis}\:{at}\:{B}.{find}\:{the} \\ $$$${locus}\:{of}\:{the}\:{mid}\:{point}\:{of}\:{AB} \\ $$$$\left.{b}\right){find}\:\:{the}\:{equation}\:{of}\: \\ $$$${assymptotes}\:{of}…
Question Number 50977 by peter frank last updated on 22/Dec/18 $${Find}\:{interms}\:{of}\:\:{a},{b}\:{the} \\ $$$${value}\:{of}\:{c}\:{which}\:{makes} \\ $$$${the}\:{line}\:{y}={mx}+{c} \\ $$$${a}\:{tangent}\:{to}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{ax}.{also}\:{obtain}\:{the}\: \\ $$$${coordinate}\:{of}\:{the}\:{point}\:{of} \\ $$$${contact} \\…