1. Understanding the Ellipse and its Parameters

To solve this problem, we must first recall the fundamental properties and definitions of an ellipse.

• Standard Equation: We typically consider an ellipse centered at the origin $(0,0)$ with its major axis along the x-axis. Its standard equation is: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ Here, $a$ represents the length of the semi-major axis (half the length of the major axis), and $b$ represents the length of the semi-minor axis (half the length of the minor axis). For an ellipse, it is always true that $a > b > 0$.

• Foci: The foci are two fixed points inside the ellipse, conventionally denoted by $F$ and $F'$. Their coordinates are $F(ae, 0)$ and $F'(-ae, 0)$, where