Ellipses

Front

What is an ellipse?

Back

An ellipse is a geometric shape that looks like a stretched circle, defined as the set of points where the sum of the distances from two fixed points (foci) is constant.

Front

What are the major and minor axes of an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter, perpendicular to the major axis.

Front

How do you find the center of an ellipse given its equation?

Back

For an ellipse in standard form (x-h)²/a² + (y-k)²/b² = 1, the center is at the point (h, k).

Front

What is the relationship between a, b, and c in an ellipse?

Back

In an ellipse, c² = a² - b², where a is the semi-major axis, b is the semi-minor axis, and c is the distance from the center to each focus.

Front

What does the term 'vertices' refer to in the context of an ellipse?

Back

Vertices are the points on the ellipse where it intersects the major axis.

Front

How do you determine the length of the major axis from the semi-major axis?

Back

The length of the major axis is twice the length of the semi-major axis (2a).

Front

What is the standard form of the equation of a horizontal ellipse?

Back

The standard form is (x-h)²/a² + (y-k)²/b² = 1, where a > b.

Front

What is the standard form of the equation of a vertical ellipse?

Back

The standard form is (x-h)²/b² + (y-k)²/a² = 1, where a > b.

Front

How do you find the foci of an ellipse?

Back

The foci are located at (h ± c, k) for a horizontal ellipse and (h, k ± c) for a vertical ellipse.

Front

What is the significance of the eccentricity of an ellipse?

Back

Eccentricity (e) measures how much an ellipse deviates from being circular; it is calculated as e = c/a.