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The center of the ellipse is at the point (-3,-3).
The major axis is horizontal line y= -3.
The major semi-axis is of the length a= = 5.
The focal distance 2c is equal to 2c = 0 - (-6) = 6.
So, the eccentricity of the ellipse is 3: c = 3 = .
It implies 9 = = ; so, b^2 = 25 - 9 = 16 and b = 4.
Thus the minor semi-axis is b= 4.
Then the equation of the ellipse is
+ = 1, or
+ = 1.
Solved.
Your prerequisite is the lesson
- Ellipse definition, canonical equation, characteristic points and elements
in this site.
Your sample lessons are
- 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
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".