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 coordinates of the center of an ellipse?

Back

The center of an ellipse is the midpoint between its two foci and is represented as (h, k) in the standard form of the ellipse equation.

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 (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

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 (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

What do 'a' and 'b' represent in the ellipse equation?

Back

In the ellipse equation, 'a' represents the length of the semi-major axis, and 'b' represents the length of the semi-minor axis.

Front

How do you find the foci of an ellipse?

Back

The foci can be found using the formula c = √(a² - b²), where c is the distance from the center to each focus.

Front

What is the length of the major axis of an ellipse?

Back

The length of the major axis is 2a, where 'a' is the length of the semi-major axis.

Front

What is the length of the minor axis of an ellipse?

Back

The length of the minor axis is 2b, where 'b' is the length of the semi-minor axis.

Front

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

Back

In an ellipse, the relationship is given by the equation c² = a² - b².

Front

What are the vertices of an ellipse?

Back

The vertices are the endpoints of the major axis, located at (h ± a, k) for a horizontal ellipse and (h, k ± a) for a vertical ellipse.