SOLUTION: find the area bounded by the curve 9x^2 + 25y^2 + 18x - 100y = 116

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: find the area bounded by the curve 9x^2 + 25y^2 + 18x - 100y = 116      Log On


   

Question 1086306: find the area bounded by the curve 9x^2 + 25y^2 + 18x - 100y = 116
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
Transform the given general equation of an ellipse to the standard form by completing the squares:


9x%5E2+%2B+25y%5E2+%2B+18x+-+100y = 116  ====>

9%2A%28x%2B1%29%5E2+%2B+25%2A%28y-2%29%5E2 = 116+%2B+9+%2B+100  ====>

9%2A%28x%2B1%29%5E2+%2B+25%2A%28y-2%29%5E2 = 225  ====>  (divide by 225 both sides)  ====>  

%28x%2B1%29%5E2%2F%28%28225%2F9%29%29 + %28y-2%29%5E2%2F%28%28225%2F25%29%29 = 1  ====>

%28x%2B1%29%5E2%2F%28%2815%2F3%29%5E2%29 + %28y-2%29%5E2%2F%28%2815%2F5%29%5E2%29 = 1.

%28x%2B1%29%5E2%2F5%5E2 + %28y-2%29%5E2%2F3%5E2 = 1.


Ellipse centered at ((-1),2) with semi-axes 5 (major semi-axis) and 3 (minor semi-axis).


The area is  pi%2A5%2A3 = 15%2Api square units.


See relevant 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
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".