Equations of Circles and Ellipses

Front

What is the standard form of the equation of a circle?

Back

(x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

What does the center of an ellipse represent?

Back

The center of an ellipse is the midpoint between its two foci and is the point from which the ellipse is symmetrically arranged.

Front

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

Back

In the equation (x-h)² + (y-k)² = r², the radius r is the square root of the right side of the equation.

Front

What is the relationship between the axes of an ellipse?

Back

The major axis is the longest diameter, while the minor axis is the shortest diameter, both intersecting at the center.

Front

What is the formula for the area of a circle?

Back

A = πr², where r is the radius.

Front

What is the formula for the area of an ellipse?

Back

A = πab, where a is the semi-major axis and b is the semi-minor axis.

Front

What does the term 'foci' refer to in the context of ellipses?

Back

Foci are two fixed points located along the major axis of an ellipse, from which the sum of the distances to any point on the ellipse is constant.

Front

How do you determine 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 equation of a circle with center (0, 0) and radius 5?

Back

x² + y² = 25.

Front

What is the equation of an ellipse centered at the origin with semi-major axis 4 and semi-minor axis 3?

Back

(x²/16) + (y²/9) = 1.