   Chapter 10.6, Problem 41E

Chapter
Section
Textbook Problem

# Finding a Polar Equation In Exercises 39-44. Find a polar equation for the conic with its focus at the pole and the given vertex or vertices.Conic Vertex or VerticesEllipse ( 2 , 0 ) ,         ( 8 , π )

To determine

To calculate: The polar form of the equation for the ellipse having its focus at the pole and the vertices are (8,π) and (2,0).

Explanation

Given:

The conic is ellipse having its vertices (8,π) and (2,0).

Formula used:

The polar form of the equation for the ellipse having its focus at the pole is:

r=ed1+ecosθ

Here e is the eccentricity and d is the distance from the focus to its directrix.

Calculation:

Take the first vertex,

(r,θ)=(8,π)

Now, put these values in the formula. Then,

r=ed1+ecosθ8=ed1+ecosπ8=ed1e

So,

ed=8(1e) …… (1)

Now, take the second vertex,

(r,θ)=(2,0)

Now, put these values in the formula

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