Ellipses

Front

What is an ellipse?

Back

An ellipse is a geometric shape that resembles a flattened circle, defined as the set of points where the sum of the distances to two fixed points (foci) is constant.

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, such that the sum of the distances from any point on the ellipse to these two points is constant.

Front

What is the major axis of an ellipse?

Back

The major axis is the longest diameter of the ellipse, passing through both foci and the center.

Front

What is the minor axis of an ellipse?

Back

The minor axis is the shortest diameter of the ellipse, perpendicular to the major axis at the center.

Front

How do you find the center of an ellipse?

Back

The center of an ellipse can be found at the midpoint of the major and minor axes.

Front

What is the standard form of the equation of an ellipse centered at the origin?

Back

The standard form is (x^2/a^2) + (y^2/b^2) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis.

Front

What is the relationship between the lengths of the axes and the foci of an ellipse?

Back

The distance from the center to each focus (c) is related to the lengths of the semi-major (a) and semi-minor (b) axes by the equation c^2 = a^2 - b^2.

Front

What are the vertices of an ellipse?

Back

The vertices of an ellipse are the points where the ellipse intersects the major axis.

Front

How do you determine the lengths of the major and minor axes from the standard form of an ellipse?

Back

In the standard form (x^2/a^2) + (y^2/b^2) = 1, the length of the major axis is 2a and the length of the minor axis is 2b.

Front

What is the eccentricity of an ellipse?

Back

Eccentricity (e) is a measure of how much an ellipse deviates from being circular, calculated as e = c/a, where c is the distance from the center to a focus.