In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0); y-intercepts: -3 and 3

An ellipse is a set of points in a plane where the sum of the distances from two fixed points, called foci, is constant. The standard form of an ellipse's equation can be expressed as (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, a is the distance from the center to the vertices along the x-axis, and b is the distance along the y-axis.

The foci of an ellipse are two fixed points that help define its shape. For an ellipse centered at the origin with horizontal major axis, the foci are located at (±c, 0), where c² = a² - b². The vertices are the endpoints of the major axis, located at (±a, 0) for horizontal ellipses, and the minor axis endpoints are at (0, ±b).

Y-intercepts are points where the graph intersects the y-axis, which occur when x = 0. For the given ellipse, the y-intercepts at -3 and 3 indicate that the ellipse extends vertically to these points. This information helps determine the value of b in the standard form equation, as it represents the distance from the center to the vertices along the y-axis.