The equation you provided appears to be a form of a hyperbola. However, it seems to have a typographical error. Let's rewrite the equation correctly:
\[ y^2 - 2x^2 = 1. \]

This is a standard form of a hyperbola. In this case:

1. **Type of Conic Section**: This represents a hyperbola that opens upward and downward.

2. **Standard Form**: The standard form of a hyperbola with a vertical transverse axis is:
\[
\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1,
\]
where \( a^2 = 1 \) and \( b^2 = \frac{1}{2} \) in your equation. Therefore:
- \( a = 1 \)
- \( b = \frac{1}{\sqrt{2}} \)

3. **Center**: The center of the hyperbola is at the origin (0, 0).

4. **Transverse Axis**: The distance from the center to the vertices (along the \( y \)-axis) is \( a = 1 \). This means the vertices are at (0, 1) and (0, -1).

5. **Asymptotes**: The asymptotes of the hyperbola can be determined from the relationship between \( a \) and \( b \):
\[
y = \pm \frac{a}{b} x = \pm \sqrt{2} x.
\]

If you need further analysis or a specific computation related to this hyperbola, please let me know!