Chapter 11.2, Problem 1E

An ellipse is the set of all points in the plane for which the __________ of the distances from two fixed points F₁ and F₂ is constant. The points F₁, and F₂ are called the __________ of the ellipse.

To determine

An ellipse is the set of all points in the plane for which the sum of the distances from two fixed points $F_1$ and $F_2$ is constant. The points $F_1$ and $F_2$ are called the foci of the ellipse.

Explanation of Solution

Definition used:

“An ellipse is the set of all points in the plane, the sum of whose distance from two fixed points $F_1$ and $F_2$ is a constant. These two fixed points are called foci of the ellipse.”

Calculation:

By the definition of the ellipse stated above, conclude that a set of points in a plane, sum of whose distance from two fixed points are always constant. The fixed points are called Foci, where foci is the plural of focus.