Ellipse Review (11/15/24)

Front

What is the standard form of the equation of an ellipse centered at (h, k)?

Back

Front

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

Back

Front

How do you find the endpoints of the minor axis of an ellipse?

Back

The endpoints of the minor axis can be found by taking the center coordinates (h, k) and adding/subtracting 'b' to/from the y-coordinate: (h, k+b) and (h, k-b).

Front

If an ellipse is centered at (2, -3) with a semi-major axis of length 6, what are the coordinates of the vertices?

Back

The vertices are at (2, -3+6) = (2, 3) and (2, -3-6) = (2, -9).

Front

What is the relationship between the lengths of the major and minor axes in an ellipse?

Back

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

Front

How do you translate an ellipse in the coordinate plane?

Back

To translate an ellipse, you add or subtract values from the x and y coordinates of the center (h, k). For example, translating 2 units right and 3 units up changes (h, k) to (h+2, k+3).

Front

What is the distance between the foci of an ellipse?

Back

Front

What is the equation of an ellipse with vertices at (3, 5) and (3, -3), and a co-vertex at (5, 1)?

Back

Front

If an ellipse has its center at (2, -3) and a vertex at (2, 3), what is the length of the major axis?

Back

The length of the major axis is 12, calculated as the distance from (2, -3) to (2, 3) which is 6 units up and 6 units down.

Front

What is the significance of the co-vertices in an ellipse?

Back

Co-vertices are the endpoints of the minor axis and help define the shape of the ellipse.