a.
To show:that the asymptotes of the hyperbola are perpendicular to each other.
a.
Explanation of Solution
Given information:
The hyperbola equation is
Proof:
First find the asymptotes of the hyperbola,
Since the
So the asymptote for the hyperbola is
Since here
So the asymptotes is,
The two asymptotes will be perpendicular is there slope product is -1.
Here the slope of
And the slope of
So the product of slope of the asymptotes is
Hence the asymptotes are perpendicular.
b.
To find: the equation for the hyperbola.
b.
Answer to Problem 43E
The equation of hyperbola is
Explanation of Solution
The equation of hyperbola is
Given information:
The hyperbola foci :
The asymptotes of hyperbola are perpendicular to each other.
Concept used: if the asymptotes of hyperbola are perpendicular to each other then
Calculation: since from the given foci it is observed that the vertices of the hyperbola are on the x-axis, so the hyperbola has a horizontal transverse axis.
So the equation is of the form,
to find the equation of hyperbola, substitute
use the relation,
So the equation of hyperbola
Hence the equation of the hyperbola is
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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