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 in a plane where the sum of the distances from two fixed points (foci) is constant.

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' is the semi-major axis and 'b' is the semi-minor axis.

Front

What do 'a' and 'b' represent in the ellipse equation?

Back

'a' represents the length of the semi-major axis, and 'b' represents the length of the semi-minor axis.

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 'a', 'b', and 'c' in an ellipse?

Back

In an ellipse, the relationship is given by the equation c^2 = a^2 - b^2.

Front

What is the center of an ellipse given in the form (x-h)^2/a^2 + (y-k)^2/b^2 = 1?

Back

The center of the ellipse is the point (h, k).

Front

How do you determine if an ellipse is horizontal or vertical?

Back

If a^2 > b^2, the ellipse is horizontal; if b^2 > a^2, the ellipse is vertical.

Front

What is the length of the major axis of an ellipse?

Back

The length of the major axis is 2a.

Front

What is the length of the minor axis of an ellipse?

Back

The length of the minor axis is 2b.

Front

How do you graph an ellipse?

Back

To graph an ellipse, identify the center, lengths of the axes, and plot the foci. Then sketch the ellipse around these points.