1. Key Concepts and Standard Forms of an Ellipse

To analyze the given equation and identify the conic section, we first need to recall the standard forms of an ellipse centered at the origin and the formula for its eccentricity.

An ellipse is defined by the property that the sum of the distances from any point on the ellipse to two fixed points (foci) is constant. Its standard equation is crucial for identifying its characteristics.

• Standard Form 1 (Major axis along x-axis): $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad \text{where } a > b > 0$ Here, $a$ is the length of the semi-major