Latus Rectum of Parabola
Latus rectum of a parabola is a focal chord which is passing through the focus and is perpendicular to the axis of the parabola. The latus rectum cuts the parabola at two distinct points. For a parabola y^{2} = 4ax, the length of the latus rectum is 4a units, and the endpoints of the latus rectum are (a, 2a), and (a, 2a).
Let us learn more about the latus rectum of the parabola, its properties, terms related to it, with the help of examples, and FAQs.
What Is Latus Rectum of Parabola?
The latus rectum of a parabola is the chord that is passing through the focus of the parabola and is perpendicular to the axis of the parabola. The latus rectum of a parabola can also be understood as the focal chord which is parallel to the directrix of the parabola. The length of the latus rectum for a standard equation of a parabola y^{2} = 4ax is equal to LL' = 4a. The endpoints of the latus rectum of a Parabola are (a, 2a), (a, 2a).
The endpoints of the latus rectum of a parabola and the focus of the parabola are all collinear. The distance between the endpoints of the latus rectum is equal to the length of the latus rectum.
Latus Rectum for Standard Equations of Parabola
The following table shows the latus rectum and the ends of latus rectums for different standard equations of a parabola.
Equation of Parabola  Focus  Latus Rectum  End Points of Latus Rectum 

\(y^2 = 4ax\)  (a, 0)  x = a  (a, 2a), (a, 2a) 
\(y^2 = 4ax\)  (a, 0)  x = a  (a, 2a), (a, 2a) 
\(x^2 = 4ay\)  (0, a)  y = a  (2a, a), (2a, a) 
\(x^2 = 4ay\)  (0, a)  y = a  (2a, a), (2a, a) 
Properties of Latus Rectum of Parabola
The following properties help in a better understanding of the latus rectum of a parabola.
 The latus rectum passes through the focus of the parabola.
 The latus rectum is perpendicular to the axis of the parabola.
 The latus rectum cuts the parabola at two distinct points.
 The latus rectum of a parabola \(y^2 = 4ax\) has a length of 4a units.
 The latus rectum is of a parabola \(y^2 = 4ax\) has the end points (a, 2a), and (a, 2a).
 The latus rectum is parallel to the directrix of parabola.
 The distance of the latus rectum from the vertex of the parabola is equal to the distance of the directrix from the vertex.
Terms Related to Latus Rectum of Parabola
The following terms are related to latus rectum and help in a better understanding of the latus rectum of a parabola.
 Focus of Parabola: The focus of parabola \(y^2 = 4ax\) is (a, 0). The parabola is defined with reference to the focus of the parabola and the parabola is the locus of a point that is equidistant from the focus and directrix of the parabola.
 Vertex of Parabola: The point where the parabola cuts the axis of the parabola is the vertex of the parabola. For a parabola \(y^2 = 4ax\) the xaxis is the axis of the parabola and (0, 0) is the vertex of the parabola.
 Axis of Parabola: The axis of the parabola is a line that cuts it into two equal halves. The axis of the parabola is also the axis of symmetry of the parabola. For the parabola \(y^2 = 4ax\) the xaxis is the axis of the parabola, and for the parabola \(x^2 = 4ax\) the yaxis is the axis of the parabola.
 Directrix of Parabola: The line parallel to the latus rectum of the parabola is the directix of the parabola. For a parabola \(y^2 = 4ax\), the directrix is x + a = 0, and is a line cutting the axis of the parabola at (a, 0). Any point on the parabola is equidistant from the focus of the parabola and the directrix of the parabola.
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Examples on Latus Rectum of Parabola

Example 1: Find the latus rectum of parabola \(y^2 = 20x\).
Solution:
The given equation of a parabola is \(y^2 = 20x\).
Comparing this with the standard equation of a parabola \(y^2 = 4ax\) we have 4a = 20, and a = 5.
For the equation of a parabola \(y^2 = 4ax\) the equation of latus rectum is x = a, which is x = 5 or x + 5 = 0.
Therefore the equation of latus rectum of parabola is x + 5 = 0.

Example 2: Find the equation of a parabola having the latus rectum y + 5 = 0.
Solution:
The given equation of latus rectum is y + 5 = 0 or y = 5.
The focus of parabola having latus rectum y = a is (0, a), and the equation of parabola is \(x^2 = 4ay\).
The required equation of parabola is \(x^2 = 4 (5)y\).
Therefore the required equation of a parabola is \(x^2 = 20y\).
FAQs on Latus Rectum of Parabola
What Is Latus Rectum Of Parabola?
The focal chord drawn perpendicular to the axis of the parabola is referred to as the latus rectum of the parabola. The latus rectum is parallel to the directrix of parabola. The parabola \(y^2 = 4ax\) has a latus rectum of length 4a units, and the endpoints of the latus rectum are (a, 2a), and (a, 2a).
How To Find The Latus Rectum Of Parabola?
The latus rectum can be identified as a line that is passing through the focus and is perpendicular to the axis of the parabola.
How Many Latus Rectums Does A Parabola Have?
The parabola has only once latus rectum, since it has one focus. For the parbola \(y^2 = 4ax\) the latus rectum is passing through the focus (a, 0).
What Is The Use Of Latus Rectum Of Parabola?
The latus rectum is a focal chord which can be used to find the equation of the parabola. The length of the latus rectum is 4a units, which is useful to form the equation of parabola \(y^2 = 4ax\).
What Is The Difference Between Latus Rectum And Directrix Of Parabola?
The latus rectum passes through the focus of the parabola, and the directrix does not pass through the focus of the parabola. The latus rectum cuts the parabola at two distinct points, and the directrix is drawn outside the parabola. For a parabola \(y^2 = 4ax\) the latus rectum passes through (a, 0), and the directrix passes through (a, 0).
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