Circle and Ellipse Mini-Flashcard

Front

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

Back

Front

How do you convert a general conic equation to standard form?

Back

To convert a general conic equation to standard form, complete the square for both x and y terms, and rearrange the equation.

Front

What is eccentricity in relation to an ellipse?

Back

Front

What is the relationship between the lengths of the axes of an ellipse?

Back

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, equidistant from the center. The sum of the distances from any point on the ellipse to the foci is constant.

Front

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

Back

Front

What is the formula for the area of an ellipse?

Back

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the lengths of the semi-major and semi-minor axes are equal (a = b).

Front

How do you determine if a conic section is a circle or an ellipse?

Back

To determine if a conic section is a circle or an ellipse, check the coefficients of the squared terms. If they are equal, it is a circle; if they are different, it is an ellipse.

Front

What is the significance of the major and minor axes in an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter. They intersect at the center of the ellipse.