Ellipses and Circles Practice

Front

What is the standard form equation of an ellipse centered at the origin with a vertical major axis?

Back

The standard form is (x^2/b^2) + (y^2/a^2) = 1, where a > b.

Front

What are the vertices of an ellipse?

Back

The vertices are the endpoints of the major axis of the ellipse.

Front

How do you find the foci of an ellipse?

Back

The foci are located at (±c, 0) for a horizontal ellipse and (0, ±c) for a vertical ellipse, where c = √(a^2 - b^2).

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 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 semi-minor axis.

Front

What is the standard form equation of a circle?

Back

The standard form is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

Front

How do you determine the radius of a circle from its equation?

Back

The radius is the square root of the constant on the right side of the equation in standard form.

Front

What is the relationship between the axes of an ellipse?

Back

The major axis is longer than the minor axis; a > b.

Front

What is the definition of eccentricity in relation to ellipses?

Back

Eccentricity (e) is a measure of how much an ellipse deviates from being circular, calculated as e = c/a.

Front

What are the coordinates of the foci for a circle?

Back

For a circle, the foci coincide with the center, so they are at (h, k).