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# (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.$x = \sinh t$, $\quad y = \cosh t$

## (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

#### Topics

Parametric Equations

Polar Coordinates

### Discussion

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##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  ##### Michael J.

Idaho State University

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### Video Transcript

the problem is part a eliminated. They permitted to find a cottage in question about off the curve for a we have Why square, Once X squared, is equal to coached. His square minus synched is going when she is equal to one. This is a competition question off the cross. Have to be sketched the curve and indicated with an arrow direction, your wages, the crops to Tristan's paramilitary increases. So first notice that why is always greater than zero so we can scarce the curve as follows. This is a curve on one team quizzes. We have axe, is it tea? Once thanked me. Over, too, increases. So this direction is the direction. Wage security. It's Trish. That's permanent increases.

WZ

#### Topics

Parametric Equations

Polar Coordinates

##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  ##### Michael J.

Idaho State University

Lectures

Join Bootcamp