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 $b^2 = a^2 - c^2$,