The given equation is an equation of an ellipse. Let's analyze it in detail.

### General Form of an Ellipse:
The general form of an ellipse centered at the origin is:

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

Here, \(a\) is the semi-major axis, and \(b\) is the semi-minor axis. If \(a > b\), the ellipse is elongated along the x-axis, and if \(b > a\), it is elongated along the y-axis.

### Given Equation:
The equation you provided is:

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

Here, we can see the following:

- \( \frac{x^2}{a^2} \) corresponds to the x-term, so \(a\) is associated with the semi-major axis along the x-direction.
- \( \frac{y^2}{a^2 - c^2} \) corresponds to the y-term, so \(b^2 = a^2 - c^2\),

Explore the equation x²/a² + y²/(a²-c²) = 1, which represents an ellipse centered at the origin. This page provides a detailed analysis of ellipse equations, focusing on the relationship between semi-major axis a, semi-minor axis b, and the distance c. Suitable for advanced high school students.

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