SOLUTION: What are the steps to the following problem, Instructions: "Write an equation for each ellipse" Problem: minor axis with length 4: foci at (-5,0),(5,0) Please Help I canno

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Question 165719This question is from textbook College Algebra
: What are the steps to the following problem,
Instructions: "Write an equation for each ellipse"
Problem: minor axis with length 4: foci at (-5,0),(5,0)
Please Help I cannot seem to figure this one out.
Thank You
This question is from textbook College Algebra

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
We have to work backwards from given information to find the major axis length (a) using minor axis length (b) and foci (c).
The general equation for an ellipse centered at (h,k) is given by,
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
.
.
.
Foci for an ellipse are located at 0%2B-c
where c%5E2=a%5E2-b%5E2=5%5E2.
The length of the minor axis is 2b=4
b=2
5%5E2=a%5E2-2%5E2
25=a%5E2-4
a%5E2=29
a=sqrt%2829%29
Since the foci are symmetric about the y-axis, the ellipse is centered at (0,0).
The equation then becomes,
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
x%5E2%2F29%2By%5E2%2F4=1
4x%5E2%2B29y%5E2=116