To calculate:
The polar equation of the conic by using the following data:
Vertices:
Answer to Problem 50E
The polar equation of the ellipse is derived as
Explanation of Solution
Given information:
Conic section: Ellipse
Vertices:
Formula used:
The equation of the ellipse is given by the following expression:
Where,
Eccentricity:
Distance from the focus to pole:
The distance between the focus and vertex is given by the following expression:
The distance between the vertices is the length major axis
Calculation:
Here, the given conic section is ellipse and its vertices are
From the given data, get that horizontal axis is the major axis. So, the nearest vertex to pole is on the left side of the pole and vertical axis represents the directrix.
So the equation of the ellipse is given by the following expression:
The length major axis
Since, the nearest vertex point lies at distance of
So, distance between the focus and vertex is calculated as:
Now, distance from the focus to directrix is calculated as:
Hence, the equation of the ellipse is derived as:
Put the calculated values:
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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