Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of the minor axis: (1, 7), (7, 7)

The standard form of the ellipse is .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

(1)

If we know that and , then the coordinates of the center are, respectively:

The length of each semiaxis is, respectively:

The standard equation of the ellipse is described by the following formula:

Where:

, - Coordinates of the center of the ellipse.

, - Length of the orthogonal semiaxes.

If we know that , , and , then the standard form of the ellipse is:

b

step-by-step explanation: