SOLUTION: If x^2 + y^2 + 4x - 2y + 1 = 0, show that (x+2)^2 + (y-1)^2 = 4

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Question 1116006: If x^2 + y^2 + 4x - 2y + 1 = 0, show that (x+2)^2 + (y-1)^2 = 4
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


This is an example of completing the square -- a very useful mathematical tool that you should know.

x%5E2%2By%5E2%2B4x-2y%2B1+=+0

Group the x and y terms on the left and move the constant to the right:

x%5E2%2B4x%2By%5E2-2y+=+-1

Complete the square in both x and y -- that is, add constants (on both sides of the equation, of course!) to make perfect square trinomials in both x and y:

%28x%5E2%2B4x%2B4%29%2B%28y%5E2-2y%2B1%29+=+-1%2B4%2B1+=+4

Write the perfect square trinomials as squares of binomials: %28x%2B2%29%5E2+%2B+%28y-1%29%5E2+=+4