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## Homework Statement

Identify the particle's path by finding a Cartesian equation for it . Graph the Cartesian equation . indicate the portion of the graph traced by the particle .

##x=2sinh t## , ##y=2cosh t## , ##-\infty < t < \infty##

## Homework Equations

##cosh^2 t - sinh^2 t = 1##

## The Attempt at a Solution

##sinh t = \frac{x}{2}##

Square both sides :

##sinh^2 t = \frac{x^2}{4}## (1)

##cosh t = \frac{y}{2}##

Square both sides :

##cosh^2 t = \frac{y^2}{4}## (2)

(2) - (1) :

##cosh^2 t - sinh^2 t = 1##

##\frac{y^2}{4} - \frac{x^2}{4} = 1##

put x= 0 → y=±2

Is my answer correct ?

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