SOLUTION: ​289​​(x−12)​2​​​​+​64​​(y−3)​2​​​​=1

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Question 1087046: ​289​​(x−12)​2​​​​+​64​​(y−3)​2​​​​=1
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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289%2A%28x-12%29%5E2 + 64%2A%28y-3%29%5E2 = 1.

Equivalently

%28x-12%29%5E2%2F%28%281%2F289%29%29 + %28y-3%29%5E2%2F%28%281%2F64%29%29 = 1,    which is the same as 

%28x-12%29%5E2%2F%28%281%2F17%29%5E2%29 + %28y-3%29%5E2%2F%28%281%2F8%29%5E2%29 = 1. 


Ellipse with the center at (x,y) = (12,3).


The major axis is vertical. The ellipse is taller than wide.


The major (vertical)   semi-axis has the length of a = 1%2F8 of unit.

The minor (horizontal) semi-axis has the length of b = 1%2F17 of unit.

The linear eccentricity is c = sqrt%28%281%2F8%29%5E2+-+%281%2F17%29%5E2%29 = sqrt%28289-64%29%2F%288%2A17%29%29 = 15%2F%288%2A17%29.


Having this, you can easily determine the foci of the ellipse.

See the lessons
    - 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

    - General equation of an ellipse
    - Transform a general equation of an ellipse to the standard form by completing the square
    - Identify elements of an ellipse given by its general equation

    - OVERVIEW of lessons on ellipses


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".