(A)
To prove:
The polar form of the orbit of the planet
(A)
Explanation of Solution
Given:
The planets travels in an alliptical orbit with the sun as its focus
Concept used:
The polar equation is
Calculation:
The equation of an ellipse with
The minimum distance from the sun to the planet is
The maximum distance from the sun to the planet is
For a conic with a focus at the origin
If the directrix is
Where d is a positive real number and the eccentricity is positive real number
The conic has a polar equation
(B)
To draw:
The polar form of the orbit of the planet
(B)
Explanation of Solution
Given:
The planets travels in an alliptical orbit with the sun as its focus
Concept used:
The polar equation is
Calculation:
The equation of an ellipse with
To draw the table
Test one point in each of the region formed by the graph
If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality
the region satisfies the inequality
The graph of the
(C)
To prove:
The polar form of the orbit of the planet
(C)
Explanation of Solution
Given:
The planets travels in an alliptical orbit with the sun as its focus
Concept used:
The polar equation is
Calculation:
The equation of an ellipse with
The minimum distance from the sun to the planet is
The maximum distance from the sun to the planet is
For a conic with a focus at the origin
If the directrix is
Where d is a positive real number and the eccentricity is positive real number
The conic has a polar equation
(D)
To prove:
The polar form of the orbit of the planet
(D)
Explanation of Solution
Given:
The planets travels in an alliptical orbit with the sun as its focus
Concept used:
The polar equation is
Calculation:
The equation of an ellipse with
The minimum distance from the sun to the planet is
The maximum distance from the sun to the planet is
For a conic with a focus at the origin
If the directrix is
Where d is a positive real number and the eccentricity is positive real number
The conic has a polar equation
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