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Question

# Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. Then graph the hyperbola.$x^2-2 y^2=2$

Solution

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Step 1
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The equation should be equal to $1$.

\begin{aligned} x^2-2y^2=1\\ \frac{x^2}{2}-\frac{2y^2}{2}=\frac{2}{2}&&\text{DPE}\\ \frac{x^2}{2}-y^2=1 \end{aligned}

Hence the standard form is

\begin{aligned} \frac{x^2}{2}-y^2=1 \end{aligned}

From this, we can conclude that the center is at the origin $(0,0)$, $a^2=2$, $b^2=1$ and the transverse axis is horizontal.

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