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?


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Question Number 207435 by NasaSara last updated on 15/May/24

$y = e^{t} - e^{- t} a n d x = e^{t} + e^{- t} d o e s t h i s p a r a m e t r i c e q u a t i o n r e s e m b l e s$ $c i r c l e o r e l l i p s e o r h y p e r b o l a o r p a r a b o l a a n d w h y ?$
	Answered by mr W last updated on 15/May/24

	$x^{2} - y^{2} = 4$ $\frac{x^{2}}{2^{2}} - \frac{y^{2}}{2^{2}} = 1 \Rightarrow h y p e r b o l a (b r a n c h x > 0)$
	Commented by NasaSara last updated on 15/May/24

	$t h a n k y o u$
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