Equations of hyperbolas Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.
A hyperbola with vertices (±4, 0) and foci (±6, 0)
In this problem we have to find an equation of the hyperbola with center at (0 ,0) with vertices ( 4 , 0) and foci ( 6 , 0).
Note; We know that a hyperbola with the center of its origin .For these hyperbolas , the standard form of the equation is - =1 for hyperbolas that extend right and left (or)
- =1for hyperbolas that extend up and down.
Consider , - =1 . In this case
Center is ;(0,0) , vertices are ;( a, 0) ,(-a,0) , and foci is ( ae, 0) (-ae,0).
Equations of the asymptotes are ; y = x , and y = x
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
The answer to “Equations of hyperbolas Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.A hyperbola with vertices (±4, 0) and foci (±6, 0)” is broken down into a number of easy to follow steps, and 43 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: foci, vertices, Hyperbolas, graphing, equation. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 45E from 10.4 chapter was answered, more than 262 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 45E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.