   Chapter 10.1, Problem 30E

Chapter
Section
Textbook Problem

# Finding the Standard Equation of an Ellipse In Exercises 31–36, find the standard form of the equation of the ellipse with the given characteristics. Vertices : ( 0 , 3 ) , ( 8 , 3 ) Eccentricity : 3 4

To determine

To calculate: The equation of ellipse when the provided vertices are (0, 3),(8,3) and

Eccentricity is e=34.

Explanation

Given:

The vertices (0, 3),(8,3) and eccentricity e=34.

Formula used:

The formula for the eccentricity of an ellipse is, e=ca

Calculation:

The centre of an ellipse (h, k) can be calculated with the help of mid-point method from the given vertices (0, 3),(8,3):

h+a=0ha=82h=8h=4k=3

Thus, (4,3) is the centre of the ellipse.

Now, since the eccentricity of the ellipse is given so by the general formula of eccentricity;

e=ca

So, for the provided ellipse c=3 and a=4

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