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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.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.