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

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

Back

The center (h,k) can be found from the equation (x-h)² + (y-k)² = r².

Front

What does the radius of a circle represent in its equation?

Back

The radius is the distance from the center to any point on the circle.

Front

In the equation (x-3)² + (y-2)² = 16, what is the radius?

Back

The radius is 4, since r² = 16.

Front

What is the general form of the equation of an ellipse?

Back

(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

How do you identify the vertices of an ellipse?

Back

The vertices are located at (h±a, k) and (h, k±b) for horizontal and vertical ellipses respectively.

Front

What is the difference between a circle and an ellipse?

Back

A circle has a constant radius from the center, while an ellipse has two focal points and varying distances to the perimeter.

Front

In the equation (x+2)² + (y-3)² = 4, what is the center of the circle?

Back

The center is (-2, 3).

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.

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for both x and y terms.