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 last updated on 25/Dec/18
$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${P}\left(\frac{{h}}{\mathrm{2}},\frac{{b}}{\mathrm{2}}\right) \\ $$$$\frac{{h}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }+\frac{{b}^{\mathrm{2}} }{\mathrm{4}{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{{h}^{\mathrm{2}} }{{a}^{\mathrm{2}} }=\mathrm{3} \\ $$$$\Rightarrow{h}=\sqrt{\mathrm{3}}{a} \\ $$
Commented by ajfour last updated on 25/Dec/18
$${you}\:{saw}\:{it}\:{straight}\:{Sir},\:{one}\:{might}\: \\ $$$${get}\:{lost}!\:{Thanks}. \\ $$