Circles and Ellipses

Front

What is the definition of a circle?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is the formula for the circumference of a circle?

Back

C = 2πr, where r is the radius of the circle.

Front

What is the formula for the area of a circle?

Back

A = πr², where r is the radius of the circle.

Front

What is an ellipse?

Back

An ellipse is a set of points where the sum of the distances from two fixed points (foci) is constant.

Front

What are the major and minor axes of an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter.

Front

How do you find 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 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 is the standard 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

What does it mean if the major axis of an ellipse is horizontal?

Back

It means that the longer dimension of the ellipse stretches along the x-axis.

Front

What is the relationship between the foci and the vertices of an ellipse?

Back

The distance from the center to each focus is c, and the distance from the center to each vertex is a, where c² = a² - b².