Latus Rectum
- In case of a circle, the length of latus rectum is equal to the diameter of circle.
- For an ellipse, the length is equal to twice the square of the length of conjugate axis, divided by the length of transverse axis.
- In a parabola, the length is simply four times its focal length.
How to find the equation of the parabola with latus rectum?
The length of the latus rectum is given by 4a. The equation of the parabola with vertex at the origin, focus at (a,0) and directrix x = -a is y 2 = 4ax. Find the equation of the parabola with latus rectum joining points (4, 6) and (4,-2). Given latus rectum joining the points (4, 6) and (4, -2). Equation of parabola is y 2 = 4ax.
How do you find the equation of a 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 y2 = 4ax y 2 = 4 a x.
What is the length of latus rectum of a hyperbola?
Latus rectum of a hyperbola is defined analogously as in the case of parabola and ellipse. The ends of the latus rectum of a hyperbola are (ae, ±b 2/a 2), and the length of the latus rectum is 2b 2/a.
What is latus rectum in math?
Latus Rectum 1 Latus Rectum Definition. In the conic section, the latus rectum is the chord through the focus, and parallel to the directrix. 2 Length of Latus Rectum of Parabola. Let the ends of the latus rectum of the parabola, y 2 =4ax be L and L’. ... 3 Length of Latus Rectum of Hyperbola. ... 4 Latus Rectum of Conic Sections. ...
How do you find the Latus point of a 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 y2 = 4ax is equal to LL' = 4a. The endpoints of the latus rectum of a Parabola are (a, 2a), (a, -2a).
How do you get the length of the latus rectum of a parabola?
The length of the latus rectum in a parabola is equal to four times the focal length....Length of the Latus Rectum of Hyperbola.Conic SectionLength of the Latus RectumEnd of the Latus RectumY2 = 4ax4aL= ( a, 2a) , L' (a, -2a)3 more rows
How do you find the two points of the latus rectum of a parabola?
1:4511:22Find two points that define the latus rectum given the vertex ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipNow if you want to find the points that define the latus rectum you can get them right off the graphMoreNow if you want to find the points that define the latus rectum you can get them right off the graph. Or you can use the x value for this which is negative 2 comma 0. And we want to plug in 0.
How do you find the 4p of a parabola?
18:5934:54Finding The Focus and Directrix of a Parabola - Conic Sections - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo that's going to be the distance. Between those two points the length of the latus rectum as we'veMoreSo that's going to be the distance. Between those two points the length of the latus rectum as we've considered before it's always going to be equal to 4p. And since p is 1 this is going to equal 4..
What is the parabola formula?
The parabola equation in its vertex form is y = a(x - h)² + k , where: a — Same as the a coefficient in the standard form; h — x-coordinate of the parabola vertex; and. k — y-coordinate of the parabola vertex.
What is the length of the latus rectum of the curve X² =- 12y?
54. What is the length of the latus rectum of the curve x2 = –12y? Solution: 55.
What does Latus mean?
the side1. The section of flesh on the body of a person or an animal between the last rib and the hip; the side. 2. A cut of meat from the flank of an animal.
How do you find the vertex of a latus rectum?
10:1511:44Find two points that define the latus rectum given Vertex (0,0 ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd now to get the points of the latus rectum. I just plug in and my a is four. I'm just gonna plugMoreAnd now to get the points of the latus rectum. I just plug in and my a is four. I'm just gonna plug it in to my equation y squared. Goes negative four x fours which is my ax. So Y squared it.
What is the P value of a parabola?
The key is the P value. If the parabola is f(x) = a ( x - v)2 +h, the P value is P = 1/(4a). The P value is both the distance from the vertex (v,h) to the focus and the distance from the vertex to the directrix. y = h - P.
How do you find the P Given the vertex?
6:1211:45How to find the directrix, focus and vertex of a parabola - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo you just write for P equals that number that your x or y.MoreSo you just write for P equals that number that your x or y.
How do you find the length of latus rectum given the vertex and focus?
The Latus rectum of a parabola is the perpendicular line to the axis and at the focus of parabola and its length is equal to 4 times the distance between the focus and vertex of the parabola.
How do you find the length of the latus rectum of a hyperbola?
Latus Rectum of Hyperbola The Latus rectum of a hyperbola is defined as a line segment perpendicular to the transverse axis through any of the foci and whose ending point lies on the hyperbola. The length of the latus rectum of a hyperbola is 2b²/a.
Latus Rectum Definition
In the conic section, the latus rectum is the chord through the focus, and parallel to the directrix. The word latus rectum is derived from the Latin word “latus” which means “side”, and the “rectum” which means “straight”. Half the latus rectum is called the semi latus rectum. The diagram above shows the latus rectum of a parabola.
Length of Latus Rectum of Parabola
Let the ends of the latus rectum of the parabola, y 2 =4ax be L and L’. The x-coordinates of L and L’ are equal to ‘a’ as S = (a, 0)
Length of Latus Rectum of Hyperbola
Latus rectum of a hyperbola is defined analogously as in the case of parabola and ellipse.
Latus Rectum of Conic Sections
The summary for the latus rectum of all the conic sections are given below:
Latus Rectum of a 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.
Latus Rectum of a Ellipse
The latus rectum of an ellipse is a line passing through the foci of the ellipse and is drawn perpendicular to the transverse axis of the ellipse. The latus rectum of an ellipse is also the focal chord which is parallel to the directrix of the ellipse. The ellipse has two foci and hence the ellipse has two latus rectums.
Latus Rectum of a Hyperbola
The latus rectum of a hyperbola is a line passing through the foci of the hyperbola and is drawn perpendicular to the transverse axis of the hyperbola. The latus rectum of a hyperbola is also the focal chord which is parallel to the directrix of the ellipse. The hyperbola has two foci and hence the hyperbola has two latus rectums.
FAQs on Latus Rectum
A latus rectum is a straight line passing through the focus of the parabola and is perpendicular to the axis of the parabola. The latus rectum of the parabola is the focal chord which is parallel to the directrix of a parabola. The prabola has only one latus rectum, but the ellipse and hyperbole have two latus rectums.
What is Latus Rectum of Parabola?
Latus Rectum is a line segment perpendicular to the axis of the parabola, through the focus and whose endpoints lie on the parabola.
How is a parabola formed?
A parabola is a plane curve formed by a point moving such that its distance from a fixed point is equal to its distance from a fixed-line. The fixed-line is the directrix of the parabola and the fixed point F is the focus. As far as JEE is concerned, parabola is an important topic in conics.
How to find the parabola when it opens vertically?
And if the parabola opens horizontally (which can mean the open side of the U faces right or left), you'll use this equation: x = a (y - k)2 + h .
What is the formula for a parabola?
If you see a quadratic equation in two variables, of the form y = ax2 + bx + c , where a ≠ 0, then congratulations! You've found a parabola. The quadratic equation is sometimes also known as the "standard form" formula of a parabola.
What is a parabola in math?
In math terms, a parabola the shape you get when you slice through a solid cone at an angle that's parallel to one of its sides, which is why it's known as one of the "conic sections.".
Focus
The focus ‘or’ foci are fixed points from which the conic sections are constructed. Ellipses and hyperbolas have two foci, while circles and parabolas have one focus each.
Directrix
The directrix is a fixed line that is used to construct a conic section. Every point on the conic is at a certain distance from the focus and from the directrix. The ratio of these distances, is called the eccentricity of the conic and determines its type.
Transverse Axis
The axis passing through the foci and connecting the vertices of a conic section is said to be the major axis. In the case of the ellipse, this is also called the major axis.
Conjugate Axis
The axis passing through the centre and perpendicular to the transverse axis is said to be the conjugate axis. In the case of an ellipse, this axis is called the minor axis.
Latus Rectum
The latus rectum is the chord that passes through the focus of a conic section, and is parallel to the directrix. For each conic section, the latus rectum has a definite length that can be written in terms of axis lengths as given below
Ellipse
Let us consider a standard ellipse, centred on the origin, and major axis along the x-axis. Its equation is given by
Circle
As the circle is a special case of the ellipse, with major and minor axis equal in length of the radius , we have,
