Chapter 11.3, Problem 1E

A hyperbola 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 hyperbola.

To determine

To fill: A hyperbola is the set of all points in the plane for which the ______ of the distances from the final points $F_1$ and $F_2$ is constant. The points $F_1$ and $F_2$ are called the ______ of the hyperbola.

Answer to Problem 1E

A hyperbola is the set of all points in the plane for which the difference of the distances from the final points $F_1$ and $F_2$ is constant. The points $F_1$ and $F_2$ are called the foci of the hyperbola.

Explanation of Solution

Definition used:

“A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed points $F_1$ and $F_2$ is a constant. These two fixed points $F_1$ and $F_2$ are called the foci of the hyperbola.”

Calculation:

By the definition stated above, it is clear that hyperbola is set of all points in a plane whose difference of the distances from two fixed points $F_1$ and $F_2$ are called foci of the hyperbola.