Question Number 207435 by NasaSara last updated on 15/May/24
$${y}={e}^{{t}} −{e}^{−{t}} \:{and}\:{x}\:=\:{e}^{{t}} +{e}^{−{t}} \:{does}\:{this}\:{parametric}\:{equation}\:{resembles} \\ $$$$\:{circle}\:{or}\:{ellipse}\:{or}\:{hyperbola}\:{or}\:{parabola}\:{and}\:{why}? \\ $$
Answered by mr W last updated on 15/May/24
$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{4} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }−\frac{{y}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }=\mathrm{1}\:\Rightarrow{hyperbola}\:\left({branch}\:{x}>\mathrm{0}\right) \\ $$
Commented by NasaSara last updated on 15/May/24
$${thank}\:{you} \\ $$