Problem 61 - College Algebra

Question

What is an ellipse?

Step-by-Step Solution

Answer

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances from two fixed points (the foci) is a constant. It is characterized by two axes (major and minor) and two foci.

Step 1: Define an Ellipse

An ellipse is a type of conic section that is not a circle but closely related to it. This shape is formed by a plane intersecting a cone. It is a curve consisting of all points for which the sum of its distances from two fixed points, called foci, is constant.

Step 2: Describe the Properties of an Ellipse

The main properties of an ellipse include: 1) The sum of distances of any point on the ellipse from two fixed points (foci) is always constant. 2) The longest diameter is called the major axis, while the shortest diameter is the minor axis. 3) The points at the ends of the major axis are called vertices.

Step 3: Explanation of Major and Minor Axes

The Major Axis is the longest diameter of the ellipse. It passes through the foci. The minor Axis is the shortest diameter of the ellipse. It is perpendicular to the major axis.

Step 4: Explanation of Foci

The two fixed points inside the ellipse are called foci. They are always located along the major axis. For any point on the ellipse, the sum of the distances to the foci is the same.