Concept explainers
To graph: The equation of parabola
Explanation of Solution
Given information:
The standard form of equation of parabola
Graph:
Consider the standard form of equation of parabola
For
For
For
For
On the Cartesian plane plot the parabolas.
The result obtained on screen is provided below,
The red curve represents
Interpretation:
As the value of p increase from 1 to 4 the graph becomes wider than the previous one.
To calculate: The focus of the parabola
Answer to Problem 84E
The focus of the parabola
Explanation of Solution
Given information:
The standard form of equation of parabola
Formula used:
The focus of the parabola of the form
Calculation:
Consider the standard form of equation of parabola
For
For
For
For
Recall thatfocus of the parabola of the form
For
For
For
For
Thus, the focus of the parabola
To calculate: The length of latus rectum of the parabola
Answer to Problem 84E
The length of latus rectum of the parabola
Explanation of Solution
Given information:
The standard form of equation of parabola
Formula used:
The focus of the parabola of the form
Calculation:
Consider the standard form of equation of parabola
Recall thatfocus of the parabola of the form
For
Therefore, there are two points
For
Therefore, there are two points
For
Therefore, there are two points
For
Therefore, there are two points
The length of latus rectum of parabola of the form
Thus, the length of latus rectum of the parabola
To describe: The use of latus rectum to sketch the parabola.
Answer to Problem 84E
The length of latus rectum is used to identity that how narrow or shallow the parabola is.
Explanation of Solution
Given information:
The standard form of equation of parabola
Consider the standard form of equation of parabola
Recall thatfocus of the parabola of the form
Recall that the length of latus rectum is
The length of latus rectum is used to identity that how narrow or shallow the parabola is.
When a parabola is to be sketched, first plot the vertex and focus of the parabola. Then plot the two points on the parabola that connects the line segment of latus rectum.
At the end join the two points with the vertex to construct the parabola.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning