Find the eccentricity of the hyperbola given by equations `x=(e^t+e^(-1))/2a n dy=(e^t-e^(-1))/3,t in Rdot`
Text Solution
AI Generated Solution
To find the eccentricity of the hyperbola given by the equations \( x = \frac{e^t + e^{-t}}{2a} \) and \( y = \frac{e^t - e^{-t}}{3} \), we can follow these steps:
### Step 1: Rewrite the equations
From the given equations, we can express them in terms of \( e^t \) and \( e^{-t} \):
- For \( x \):
\[
2x = e^t + e^{-t}
\]
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Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-t))/2 and y=(e^t-e^(-t))/3,t in R .
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