SOLUTION: Find an equation of the ellipse that has center (5,-1) , a major axis of length 4 , and endpoint of minor axis (6,-1) .

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Question 1137076: Find an equation of the ellipse that has center (5,-1)
, a major axis of length 4
, and endpoint of minor axis (6,-1)
.
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
Minor axis is horizontal; minor semi-axis has the length 6-5 = 1 unit.


Major axis is vertical; major semi-axis has the length 4/2 = 2.


The ellipse is taller than wide.


The equation is 


    %28x-5%29%5E2%2F1%5E2 + %28y-%28-1%29%29%5E2%2F2%5E2 = 1,   or, equivalently


    %28x-5%29%5E2%2F1%5E2 + %28y%2B1%29%5E2%2F2%5E2 = 1.       ANSWER

Solved.

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To see the theory and a set of solved problems on this subject, look into the lessons in this site
    - Ellipse definition, canonical equation, characteristic points and elements

    - Standard equation of an ellipse
    - Identify elements of an ellipse given by its standard equation
    - Find the standard equation of an ellipse given by its elements

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.