The equation you provided is the standard form of an ellipse:

\[
\frac{y^2}{a^2} + \frac{x^2}{b^2} = 1
\]

### Key Features of the Ellipse:
1. **Center:** The center of this ellipse is at the origin (0, 0).
2. **Axes:**
   - **Major Axis:** The length of the major axis is \( 2a \) (aligned along the y-axis).
   - **Minor Axis:** The length of the minor axis is \( 2b \) (aligned along the x-axis).
3. **Vertices:**
   - Along the y-axis: \((0, \pm a)\)
   - Along the x-axis: \((\pm b, 0)\)
4. **Foci:** The foci of the ellipse are located along the y-axis at \((0, \pm c)\), where \( c = \sqrt{a^2 - b^2} \) if \( a > b \).
5. **Eccentricity:** The eccentricity \( e \) is calculated as \( e = \frac{c}{a} \), which gives a measure of how "stretched" the ellipse is.

Would you like more details on any specific aspect of this ellipse? 

### Related Questions:
1. How do you find the area of an ellipse given \( a \) and \( b \)?
2. What happens to the shape of the ellipse if \( a = b \)?
3. How can you derive the equation of the ellipse if it's centered at a different point?
4. What is the significance of the eccentricity in the context of an ellipse?
5. How do you plot the ellipse using the given equation?

**Tip:** When \( a > b \), the ellipse is elongated along the y-axis, and when \( b > a \), it's elongated along the x-axis.

Explore the standard form of an ellipse equation y²/a² + x²/b² = 1 with detailed explanations of its center, axes, vertices, foci, and eccentricity. Suitable for high school students studying conic sections and algebra.

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