Understanding the Parabola: Equations, Properties, and Examples
Parabola as a Geometric Locus
The parabola is defined as the geometric locus of a point that moves in a plane such that its distance from a fixed line (the directrix) is equal to its distance from a fixed point (the focus, denoted by F).
The following figure illustrates the elements of a parabola:
Where:
- F is the focus of the parabola.
- V is the vertex of the parabola.
- The segment represented by this image
is the directrix. - The segment represented by this image
is the latus rectum (LR). - The segment represented
Equations of the Circumference: Canonical, General & Polar Forms
Circumference as a Geometric Locus
A geometric locus is a set of points that satisfy specific geometric conditions. The geometric locus of the circumference is the set of all points that are equidistant (a distance of r) from a fixed point called the center.
Example: Finding the Geometric Locus
Determine the geometric locus that describes a point moving a distance of 4 units around a fixed point with coordinates (0,0).
Steps
- Identify the fixed point: The fixed point is (0, 0) on the plane.
- Draw points:
Equations of a Circumference: A Comprehensive Guide
Circumference as Geometric Locus
The geometric locus is a group of points that satisfy certain geometric conditions. The geometric locus of the circumference is the group of points that are at the same distance r from a point called the center.
Example
Determine the geometric locus that describes a point that moves a distance of 4 units around a fixed point with coordinates (0,0).
Steps
- Identify the fixed point on the plane.
- Draw a point at a distance of 4 units to each of the four cardinal points.
- Join
Statistical Quality Control for Computer Lab Availability
1. Graphic Frequency
Note that for the development of the report, 7 days were tabulated in the given table, which corresponds to a representative sample of the state of the computer lab.
With the tabulated data, we proceeded to perform frequency graphs to demonstrate the problem that affected the laboratory, which corresponds to the non-availability of computers. We built a frequency graph for the 210 observations obtained during the 7 days, through all three shifts (morning, afternoon, and evening)
Read MoreUnderstanding Lines: Equations, Slopes, and Parallelism
The Line as a Geometric Locus
The line is a group of points that can be enlarged infinitely in both directions. A straight line is also defined as “a geometric locus of a point that moves on the plane in a way that, when located in any two positions, its slope m results as the same” (Vázquez, 2007).
Example: Graphing a Line
On the plane, graph the line that passes through the points (-3, 4) and (6, 3).
Steps
- Procedure: Graph the given points on the Cartesian plane.
- Procedure: Graph a line that joins
Introduction to Matrices: Types, Operations, and Properties
Gauss
Calculating the Inverse of a Matrix
Let A = (aij) be a square matrix of order n. To calculate the inverse of A, denoted as A-1, follow these steps:
Step 1: Building the Augmented Matrix
Build the n x 2n matrix M = (A | I), where A is in the left half of M and the identity matrix I is on the right.
Step 2: Gaussian Elimination
Keep the first row of M as it is. Below the first main diagonal element, a11 (which we’ll call the pivot), put zeros. Then operate as shown in the following example.