SOLUTION: Find the center and radius of the circle 3x^2+y^2-6x+4y-4=0

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Question 83212: Find the center and radius of the circle
3x^2+y^2-6x+4y-4=0
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given conic

Add 4 to both sides

Group like terms

Factor a 3 out of the first parenthesis
and factor a 1 out of the second parenthesis.

Now we must complete the individual squares inside the parenthesis:

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For instance to complete , take half of -2 and square it (ie to get 1. Now add 1 inside the parenthesis like this:

Since you really added to the entire left side, we must add to the right side also. Now lets complete

In order to complete , take half of 4 and square it (ie to get 4. Now add 4 inside the parenthesis like this:

Since you really added to the entire left side, we must add to the right side also.

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Complete the individual squares by taking half of the 2nd coefficient and squaring it (remember to add to both sides).

Combine like terms on the right side

Factor the individual groups on the left side

Divide both sides by 11

Break up the fraction into standard form

So the equation is an ellipse where the center is (1,-2)
Here's the graph
graph of with the center (1,-2)