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

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