Conics Ellipse

Front

What is an ellipse?

Back

An ellipse is a geometric shape that looks like a stretched circle. It is defined as the set of all points where 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. They represent the maximum extent of the ellipse in the direction of the major axis.

Front

What are the foci of 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 two foci is constant.

Front

How do you find the center of an ellipse?

Back

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

Front

What is the equation of a standard ellipse centered at the origin?

Back

The equation is (x^2/a^2) + (y^2/b^2) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis.

Front

What is the difference between 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, perpendicular to the major axis.

Front

How do you determine the length of the major axis of an ellipse?

Back

The length of the major axis is 2a, where 'a' is the length of the semi-major axis.

Front

How do you determine the length of the minor axis of an ellipse?

Back

The length of the minor axis is 2b, where 'b' is the length of the semi-minor axis.

Front

What is the relationship between the foci, vertices, and the lengths of the axes in an ellipse?

Back

The distance from the center to each focus (c) is related to the lengths of the semi-major (a) and semi-minor (b) axes by the equation c^2 = a^2 - b^2.

Front

What does it mean if an ellipse is 'stretched' in a particular direction?

Back

If an ellipse is 'stretched' vertically, it means that the length of the semi-major axis (a) is greater than the length of the semi-minor axis (b), making it taller than it is wide.