Question Number 51279 by ajfour last updated on 25/Dec/18 | ||
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Commented by ajfour last updated on 25/Dec/18 | ||
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$${If}\:{both}\:{ellipses}\:{have}\:{the}\:{same} \\ $$$${parameters}\:{a}\:{and}\:{b},\:{find}\:\boldsymbol{{h}}. \\ $$ | ||
Answered by mr W last updated on 25/Dec/18 | ||
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$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${P}\left(\frac{{h}}{\mathrm{2}},\frac{{b}}{\mathrm{2}}\right) \\ $$$$\frac{{h}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }+\frac{{b}^{\mathrm{2}} }{\mathrm{4}{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{{h}^{\mathrm{2}} }{{a}^{\mathrm{2}} }=\mathrm{3} \\ $$$$\Rightarrow{h}=\sqrt{\mathrm{3}}{a} \\ $$ | ||
Commented by ajfour last updated on 25/Dec/18 | ||
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$${you}\:{saw}\:{it}\:{straight}\:{Sir},\:{one}\:{might}\: \\ $$$${get}\:{lost}!\:{Thanks}. \\ $$ | ||