Ellipses and Circles Practice

Front

What is the standard form equation of an ellipse?

Back

The standard form equation of an ellipse is given by (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 are the vertices of an ellipse?

Back

The vertices of an ellipse are the points where the ellipse intersects its major axis. They are located at a distance 'a' from the center along the major axis.

Front

What are the co-vertices of an ellipse?

Back

The co-vertices of an ellipse are the points where the ellipse intersects its minor axis. They are located at a distance 'b' from the center along the minor axis.

Front

How do you find the eccentricity of an ellipse?

Back

The eccentricity (e) of an ellipse is calculated using the formula e = √(1 - (b²/a²)), where 'a' is the semi-major axis and 'b' is the semi-minor axis.

Front

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

Back

As the eccentricity of an ellipse increases (closer to 1), the ellipse becomes more elongated, and the lengths of the axes differ more significantly.

Front

What is the general shape of an ellipse?

Back

An ellipse is a closed curve that resembles a flattened circle, defined as the set of points where the sum of the distances to two fixed points (foci) is constant.

Front

How do you graph an ellipse given its equation?

Back

To graph an ellipse, identify the center, vertices, and co-vertices from the equation, then plot these points and sketch the curve smoothly connecting them.

Front

What is the significance of the foci in an ellipse?

Back

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

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 convert the general form of an ellipse to standard form?

Back

To convert the general form Ax² + By² + Cx + Dy + E = 0 to standard form, complete the square for both x and y terms.