Question Number 51614 by peter frank last updated on 29/Dec/18 $${Prove}\:{that}\:{length}\:{of} \\ $$$${lactus}\:{rectum}\:{when}\: \\ $$$${directrix}\:{are}\:{parallel}\:{to} \\ $$$${y}−{axis}\:{is}\: \\ $$$${y}_{\mathrm{1}} −{y}_{\mathrm{2}} =\frac{\mathrm{2}{b}^{\mathrm{2}} }{{a}} \\ $$ Answered…
Question Number 51612 by peter frank last updated on 29/Dec/18 $${Find}\:{the}\:{equation}\:{of} \\ $$$${the}\:{ellipse}\:{with}\:{ecentricity} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:{the}\:{focus}\:\left(\mathrm{2},\mathrm{1}\right) \\ $$$${Does}\:{the}\:{line}\:{x}=\mathrm{3}\:{touches} \\ $$$${ellipse}.{if}\:{so}\:{at}\:{what}\: \\ $$$${point}?{if}\:{line}\:{x}=\mathrm{5}\:{is}\:{the} \\ $$$${line}\:{of}\:{direction}. \\ $$…
Question Number 51613 by peter frank last updated on 29/Dec/18 $${Prove}\:{that}\:{the}\:{perpendicilar} \\ $$$${tangent}\:{to}\:{the}\:{ellipse} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\:{meets}\:{on}\:{the} \\ $$$${circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} +{b}^{\mathrm{2}} .…
Question Number 51588 by peter frank last updated on 28/Dec/18 $${The}\:{tangent}\:{at}\:{P}\:\:{to}\:{an}\:{ellipse} \\ $$$${meets}\:{directrix}\:{at}\:{Q} \\ $$$${prove}\:{that}\:{the}\:{line} \\ $$$${joining}\:{the}\:{corresponding} \\ $$$${focus}\:{to}\:{P}\:{and}\:{Q}\:{are} \\ $$$${perpendicular} \\ $$ Answered by…
Question Number 51590 by peter frank last updated on 28/Dec/18 $${The}\:{line}\:{y}={mx}+{c}\:{touches} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${prove}\:{that}\:{the}\:{foot}\:{of}\: \\ $$$${perpendicular}\:{from} \\ $$$${focus}\:{into}\:{this}\:{line}\:{lie}\:{on} \\ $$$${auxillary}\:{circle}\:…
Question Number 51492 by peter frank last updated on 27/Dec/18 $${For}\:{ellipse}\: \\ $$$$\mathrm{16}{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} +\mathrm{96}{x}−\mathrm{8}{y}−\mathrm{84}=\mathrm{0} \\ $$$${find} \\ $$$$\left.{i}\right){centre} \\ $$$$\left.{ii}\right){verteces} \\ $$$$\left.{iii}\right){focus} \\ $$$$\left.{iv}\right){directrix}…
Question Number 51489 by peter frank last updated on 27/Dec/18 $${Given}\:{that}\:{y}={mx}+{c} \\ $$$${is}\:{equation}\:{of}\:\:{tangent} \\ $$$${to}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}\:} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${find}\:{coordinate}\:{of}\: \\ $$$${point}\:{of}\:{contact}. \\ $$…
Question Number 51485 by ajfour last updated on 27/Dec/18 Commented by ajfour last updated on 27/Dec/18 $${Regions}\:{A},\:{B},\:{C}\:{have}\:{the}\:{same}\:{area}. \\ $$$${Find}\:{equation}\:{of}\:{the}\:{parabola}. \\ $$ Terms of Service Privacy…
Question Number 182542 by cortano1 last updated on 11/Dec/22 Commented by cortano1 last updated on 11/Dec/22 $$\mathrm{Radius}\:\mathrm{semi}\:\mathrm{circle}\:\mathrm{PQR}\:=\:\mathrm{24}\:\mathrm{cm} \\ $$$$\mathrm{radius}\:\mathrm{semi}\:\mathrm{circle}\:\mathrm{BML}\:=\:\mathrm{21cm} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{ABCD}\:. \\ $$ Answered by…
Question Number 51372 by ajfour last updated on 26/Dec/18 Commented by ajfour last updated on 26/Dec/18 $${For}\:{the}\:{two}\:{coloured}\:{areas}\:{to}\:{be} \\ $$$${equal},\:{what}\:{is}\:{the}\:{slope}\:{of}\:{blue}\:{line}? \\ $$ Answered by mr W…