Q
QuestionMathematics

Find the equation of a hyperbola with foci ​(0,plus or minus^6​) and the length of the transverse axis 4. Graph the hyperbola.
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Answer

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Step 1
: Write down the standard equation for a hyperbola.

where $2a$ is the length of the transverse axis and $2c$ are the foci.
The standard equation for a hyperbola centered at the origin is:

Step 2
: Find $a$ and $c$.

We are also given that the foci are at $(0, \pm 6)$, so $c = 6$.

Final Answer

The equation of the hyperbola is \frac{x^2}{4} - \frac{y^2}{32} = 1. The graph of the hyperbola is shown above.