Latus Rectum of an Ellipse

A conic section is a curve created by the intersection of a cone’s surface with a plane in mathematics. There are three different types of conic sections. The parabola, ellipse, and hyperbola are the three types of curves. Many terms, such as focus, directrix, latus rectum, locus, asymptote, and so on, are used to describe these curves. We will further study the latus rectum of ellipse importance in depth through these notes.

What is the latus rectum?

The term ‘latus rectum’ is derived from the Latin words ‘latus’, which means ‘side’ and ‘rectum’, which means ‘straight’ in the conic section. The chord travelling across the focus and perpendicular to the directrix is the latus rectum. On the curve, the latus rectum’s terminal point is located. The semi latus rectum is made up of half of the latus rectum.

The latus rectum of an ellipse is a line drawn perpendicular to the ellipse’s transverse axis and going through the foci of the ellipse. An ellipse’s latus rectum is also the focal chord, which runs parallel to the ellipse’s directrix. Because the ellipse has two foci, it also has two latus rectums.

Latus rectum of ellipse

When a plane cuts the cone so that the plane is neither parallel nor perpendicular to the cone’s axis, nor is it parallel to the cone’s generator, an ellipse is generated. An ellipse is a conic whose eccentricity is always less than one, i.e. e 1. As a result, the ratio of the distance from the focus to the perpendicular distance from the directrix is always less than one for all points on the ellipse.

General equation of an ellipse

The length of the latus rectum of the ellipse x2/a2 + y2/b2= 1, is 2b2/a.

The ellipse’s centre lies at (0, 0).

Ellipses typically feature two focus points and, as a result, two latus recta.

Properties of the latus rectum of an ellipse

The ellipse’s latus rectum has the following key qualities.

• The principal axis of the ellipse is perpendicular to the latus rectum

• The ellipse’s latus rectum goes across the ellipse’s focus

• For an ellipse, there are two latus recta

• The ellipse is cut in two places by each latus rectum

• The ellipse’s directrix is parallel to the latus rectum.

Terms related to latus rectum of an ellipse

The terms below are connected to the latus rectum of the ellipse and might help you grasp the notion of the latus rectum of the ellipse better.

Focal chord: The focal chord of an ellipse is the line that passes through the centre of the ellipse. There are an endless number of focal chords that pass through the focus of the ellipse. The latus rectum of the ellipse is the focal chord that runs perpendicular to the ellipse’s axis.

Directrix: A directrix is a line drawn outside an ellipse that is perpendicular to the ellipse’s principal axis. The definition of an ellipse can be found using Directrix. The ellipse is the locus of a point with a distance ratio of less than one between the focus and the directrix.

Ellipse Major Axis: The ellipse’s major axis is a line that divides the ellipse into two equal halves. The major axis is a line that runs through the foci and the ellipse’s centre. The major axis endpoints are (a, 0), (-a, 0), and the length of the main axis is 2a units for an ellipse x2a2+y2b2=1.

Ellipse Minor Axis: The ellipse’s minor axis, x2a2+y2b2=1, is perpendicular to the ellipse’s main axis. The endpoints of the ellipse’s minor axis are (0, b), (0, -b), and the minor axis length is 2b units. The ellipse’s minor axis also goes through its centre.

Ellipse Vertex: An ellipse’s vertex is where the ellipse’s axis of symmetry intersects with the ellipse’s axis of symmetry. An ellipse has two vertices because it intersects its axis of symmetry at two different locations. The vertex of an ellipse is also the point of intersection of the line that passes through the ellipse’s foci and cuts it into two different points.

Conclusion

The latus rectum of an ellipse is a line drawn perpendicular to the ellipse’s transverse axis and going through the foci of the ellipse. An ellipse’s latus rectum is also the focal chord, which runs parallel to the ellipse’s directrix. Because the ellipse has two foci, it also has two latus rectums.