Conics: Ellipses

Front

What is the standard form of the equation of an ellipse centered at (h, k) with a vertical major axis?

Back

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

Front

What is the standard form of the equation of an ellipse centered at (h, k) with a horizontal major axis?

Back

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

Front

What do the variables a and b represent in the equation of an ellipse?

Back

a is the semi-major axis length, and b is the semi-minor axis length.

Front

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

Back

The center is the midpoint of the line segment connecting the vertices.

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 given by c² = a² - b².

Front

What are the coordinates of the foci of an ellipse with a vertical major axis?

Back

(h, k ± c), where c is the distance from the center to each focus.

Front

What are the coordinates of the foci of an ellipse with a horizontal major axis?

Back

(h ± c, k), where c is the distance from the center to each focus.

Front

If the vertices of an ellipse are at (0, 4) and (0, -4), what is the length of the major axis?

Back

The length of the major axis is 8.

Front

If an ellipse has a semi-major axis of length 5 and a semi-minor axis of length 3, what is the equation of the ellipse?

Back

(x - h)²/3² + (y - k)²/5² = 1.

Front

What is the definition of an ellipse?

Back

An ellipse is the set of all points such that the sum of the distances from two fixed points (foci) is constant.