# Length of the Latus Rectum of an Ellipse

The length of the latus rectum of the ellipse is .

The chord through the focus and perpendicular to the axis of the ellipse is called its latus rectum. Since the ellipse has two foci, it will have two latus recta.

Let and be the ends of the latus rectum as shown in the given diagram. Since the latus rectum passes through the focus, abscissa of and will be . Now putting in the given equation of ellipse, we have

Since , putting this value in equation (i), we have

Thus, and . The length of the latus rectum is