SOLUTION: Write an equation for the given ellipse that satisfies the following conditions. Center at (1,1); minor axis vertical, ,with length8; c=3

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Question 1149939: Write an equation for the given ellipse that satisfies the following conditions.
Center at (1,1); minor axis vertical, ,with length8; c=3

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.

Minor axis is 8 units --- hence, the minor semi-axis is b= 8/2 = 4 units.


Eccentricity c= 3 --- hence, 

    c^2 = a^2 - b^2  ===>  a^2 = c^2 + b^2 = 3^2 + 4^2 = 25  ===> a =  = 5, where "a" is the major semi-axis.


Since minor axis is vertical, the ellipse  "is wider than tall"  and  "a"  goes with x-term,  while  "b"  goes with y-terms.


Taking into account the center's position, the standard form equation of ellipse is


     +  = 1.    ANSWER

Solved.

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For associated lessons, see
    - 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
in this site.

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.




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