Chapter 10.1, Problem 33E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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;

(xâˆ’3)2a2+(yâˆ’5)2b2=1(3âˆ’3)2b2+(1âˆ’5)<

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