   Chapter 10.1, Problem 33E

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 : ( 3 , 1 ) , ( 3 , 9 ) Minor   axis   length : 6

To determine
The equation of an ellipse with the provided characteristics.

Explanation

Given: The vertices (3, 1), (3, 9) and Minor axis of length 6 for an ellipse.

Calculation: Since the provided ellipse changes its length in the y axis, so the given ellipse is of the second type with centre as the midpoint of both the vertices.

Vertices (3, 1), (3, 9)

k=9+12=5h=3+32=3

So the center is; (3, 5)

Since, the length of the minor axis is 6, so

2a=6 i.e. a=3

2b=6b=3b2=9

Now use the provided vertices (3, 1), (3, 9) to get the equation;

(x3)2a2+(y5)2b2=1(33)2b2+(15)<

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