SOLUTION: please help me solve this equation : 4(x+3)^2+49(y-4)^2=196

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Question 1170012: please help me solve this equation : 4(x+3)^2+49(y-4)^2=196
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


NOTE: You are not "solving" the equation. You are putting it in some standard form so you can identify the conic section the equation represents.

4%28x%2B3%29%5E2%2B49%28y-4%29%5E2+=+196

The equation contains x^2 and y^2 terms, both positive -- so the equation is that of an ellipse.

The standard form of the 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, or
%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2+=+1 if the major axis is vertical

To get the given equation in standard form, we only need to get "1" on the right side, by dividing everything by 196:

4%28x%2B3%29%5E2%2F196%2B49%28y-4%29%5E2%2F196+=+1
%28x%2B3%29%5E2%2F49%2B%28y-4%29%5E2%2F4+=+1
%28x-%28-3%29%29%5E2%2F7%5E2%2B%28y-4%29%5E2%2F2%5E2+=+1

The equation is of an ellipse with center (-3,4), major axis 7, and minor axis 2.