What is the formula of latus rectum of an ellipse?

Latus Rectum of Ellipse Latus rectum of the ellipse is defined as the length of the line segment perpendicular to the major axis passing through any of the foci and whose endpoint lies on the ellipse. The length of the latus rectum of an ellipse is 2b²/ a.

How do you solve the latus rectum?

Find the length of the latus rectum whose parabola equation is given as, y2 = 12x. Hence, the length of the latus rectum of a parabola is = 4a = 4(3) =12.

What is the latus rectum of above said ellipse?

The latus rectum of an ellipse is the chord of the chord of the ellipse through its one focus and perpendicular to the major axis. It is said that the length of the latus rectum of an ellipse is equal to \[{{\dfrac{1}{3}}^{rd}}\] of the major axis. We know the length of the major axis of ellipse = 2a.

What is meant by Latus Rectum?

Definition of latus rectum : a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.

What is the length of the latus rectum of the ellipse?

The length of the latus rectum of the ellipse x 2 a 2 + y 2 b 2 = 1, a > b is 2 b 2 a. The chord through the focus and perpendicular to the axis of the ellipse is called its latus rectum.

How to find the length of the latus rectum of a parabola?

Find the length of the latus rectum whose parabola equation is given as, y 2 = 12x. Since y 2 = 4ax is the equation of parabola, we get value of a: Hence, the length of the latus rectum of a parabola is = 4a = 4 (3) =12. Find the length of the latus rectum of an ellipse 4x 2 + 9y 2 – 24x + 36y – 72 = 0.

What is the abscissa of A and B in this ellipse?

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 A and B be the ends of the latus rectum as shown in the given diagram. Since the latus rectum passes through the focus, abscissa of A and B will be ae.

What is half of the latus rectum called?

Half the latus rectum is called the semi latus rectum. The diagram above shows the latus rectum of a parabola. Let the ends of the latus rectum of the parabola, y 2 =4ax be L and L’.