SOLUTION: Please help me solve this one.x^2+3y^2-2x-6y=0

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Question 1016823: Please help me solve this one.x^2+3y^2-2x-6y=0
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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Please help me solve this one.x^2+3y^2-2x-6y=0
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Solve what? 

This is an equation of an ellipse.

x%5E2%2B3y%5E2-2x-6y = x%5E2+-2x +3y%5E2+-+6y = %28x-1%29%5E2+-1 + 3%2A%28y-1%29%5E2-3.

So the original equation is equivalent to

%28x-1%29%5E2 + 3%2A%28y-1%29%5E2 = 4,  or

%28x-1%29%5E2%2F4 + %28y-1%29%5E2%2F%28%284%2F3%29%29 = 1,   or

%28x-1%29%5E2%2F%282%5E2%29 + %28y-1%29%5E2%2F%282%2Fsqrt%283%29%29%5E2 = 1.

Ellipse with the center at the point (1,1).

The major semi-axis is 2. The minor semi-axis is sqrt%283%29%2F2.