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Question 1086650: find the focus of x^2+4y^2+2x+24y++28=0
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
find the focus of x^2+4y^2+2x+24y++28=0
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I don't know what "++" means; will assume that it is "+".
 ===> (I will complete the squares for x-terms and y-terms separately) ====>
 =  ,
 +  = ,
 +  =  ,
 +  =  ,
 +  = 1.
Ellipse + = 1
The center of the ellipse is at (x,y) = (-1,-3).
The ellipse has the horizontal major axis.
The major semi-axis is 3 units long.
The minor semi-axis is  = 1.5 units long.
The linear eccentricity is  =  .
The foci are at ( , ) and ( ,).
For more details, see the lessons
- Ellipse definition, canonical equation, characteristic points and 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
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".
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