Conic Sections: Ellipse

Front

What is an ellipse?

Back

An ellipse is a set of points in a plane such that the sum of the distances from two fixed points (foci) is constant.

Front

What are the vertices of an ellipse?

Back

The vertices of an ellipse are the points where the ellipse intersects its major axis.

Front

What is the standard form of the equation of an ellipse centered at the origin?

Back

The standard form is (x^2/a^2) + (y^2/b^2) = 1, where a and b are the semi-major and semi-minor axes.

Front

How do you find the foci of an ellipse?

Back

The foci can be found using the formula c = √(a^2 - b^2), where c is the distance from the center to each focus.

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, perpendicular to the major axis.

Front

What is the center of an ellipse?

Back

The center of an ellipse is the midpoint between its foci and is also the intersection of its axes.

Front

How do you determine the length of the major and minor axes?

Back

The length of the major axis is 2a and the length of the minor axis is 2b.

Front

What is the eccentricity of an ellipse?

Back

Eccentricity (e) is a measure of how much an ellipse deviates from being circular, calculated as e = c/a.

Front

What is the equation of an ellipse with a horizontal major axis?

Back

The equation is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center.

Front

What is the equation of an ellipse with a vertical major axis?

Back

The equation is (x-h)^2/b^2 + (y-k)^2/a^2 = 1, where (h,k) is the center.