Table of Contents
Define Conic Section
A conic section is a geometric shape that is formed when a plane intersects a cone. There are four types of conic sections: circles, ellipses, parabolas, and hyperbolas.
What is Latus Rectum?
The Latus Rectum is the chord that is drawn from the focus of an ellipse to the point where the major and minor axes intersect. It is the longest chord of the ellipse.
Parabola
A parabola is a curve in mathematics that is shaped like an upside-down U. It is created by taking a point on a plane and drawing a line from that point to each point on the plane that is a certain distance away. A parabola is always symmetrical, meaning that if you fold the curve in half, the two halves will match up perfectly.
Latus Rectum of Parabola
The latus rectum is the distance from the focus to the directrix of a parabola.
General Equation of Parabola
The general equation of a parabola is:
y = a(x – h)2 + k
Where:
y is the y-coordinate of the vertex
a is the coefficient of x2
h is the x-coordinate of the vertex
k is the y-coordinate of the vertex
Length of the Latus Rectum of Parabola Derivation
There is no definitive answer to this question as the length of the latus rectum of a parabola can vary depending on the equation used to calculate it. However, a rough estimate of the length of the latus rectum for a parabola can be found using the following equation:
Latus Rectum = 2p(x_0)^2
Where p is a constant and x_0 is the coordinate of the vertex.
Latus Rectum of Parabola Formula
The latus rectum of a parabola is a line segment that is perpendicular to the directrix and has a length equal to the distance from the focus to the parabola. The latus rectum can be found using the following formula:
Latus Rectum = √(h^2 + k^2)
Hyperbola
A hyperbola is a conic section with two branches, each of which is a hyperbola. The asymptotes of a hyperbola are the lines x = ± a. The foci are at (± c, 0). The hyperbola has the equation
x2/a2 − y2/b2 = 1.
Here a and b are the lengths of the semiaxles.
Latus Rectum of Hyperbola
The latus rectum of a hyperbola is a line segment that connects the two foci of the hyperbola and has the same length as the major axis of the hyperbola.
Ellipse
An ellipse is a figure formed by two lines, called the major and minor axes, drawn from the same point and intersecting at right angles. The distance from the center of the ellipse to any point on the ellipse is called the radius.
Definition
A statement that is false, but is made to appear to be true.
An example of a false statement is “I am the best basketball player in the world.”
Shape of an Ellipse
An ellipse is a two-dimensional shape that has the following properties:
-It is symmetrical about its center.
-The sum of the distances from the center to any two points on the ellipse is the same.
-The distance from the center to any point on the ellipse is greater than the distance from that point to either of the two foci.
Properties
Name Type Description
name String The name of the origin.
url String The URL of the origin.
Latus Rectum Examples
1. The latus rectum of a parabola is the line segment that connects the focus of the parabola to the directrix.
2. The latus rectum of a hyperbola is the line segment that connects the two foci of the hyperbola.
