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WZ
Numerade Educator

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Problem 17 Easy Difficulty

(a) Eliminate the parameter to find a Cartesian equation of the curve.
(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as parameter increases.

$ x = \sinh t $, $ \quad y = \cosh t $

Answer

(a) \[
x=\sinh t, y=\cosh t \Rightarrow y^{2}-x^{2}=\cosh ^{2} t-\sinh ^{2} t=1
\]
since $y=\cosh t \geq 1,$ we have the upper branch of the hyperbola
\[
y^{2}-x^{2}=1
\]
(b) Graph

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Video Transcript

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