To show: that the polar equation of the orbit is
Explanation of Solution
Given information:
The planet travel in elliptical orbits with the sum at one focus. Assume that the focus is at the pole, the major axis lies on the polar axis, and the length of the major axis is
Given figure
Calculation:
From the above figure it is clear that the directrix is vertical and is on the left of the pole. Thus, the parametric equation of the conic is:
It is known that the distance from the center to pole is
Thus, the 2 vertices are:
Substituting in the equation,
Add both the equations
Substituting in the parametric equation:
Hence, proved.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning