SOLUTION: what conic section does the equation x^2/36+y^2/16=1 represent?

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Question 933775: what conic section does the equation x^2/36+y^2/16=1 represent?
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2F36%2By%5E2%2F16=1 always when you see it's equal to 1, you know it's an ellipse
Standard equation of an ellipse is:

%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1 (if the major axis is horizontal).

%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1 (if the major axis is vertical).
since your ellipse doesn't have any value for h and k, means h=0 and k=0 and the center is in origin (0,0)
a is the horizontal semi-axis and b the vertical semi-axis
since your a=sqrt%2836%29=highlight%286%29 and b=sqrt%2816%29=highlight%284%29, we can see that a%3Eb, so, the standard equation of your ellipse is:
%28x-0%29%5E2%2F36+%2B+%28y-0%29%5E2%2F16+=+1 (the major axis is horizontal)