Rewrite the equation x^2 + y^2 - 2x + y + 1 = 0 in (h,k) form.
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Rewrite the equation x^2 + y^2 - 2x + y + 1 = 0 in (h,k) form.

[From: ] [author: ] [Date: 12-07-13] [Hit: ]
-Because x and y are both squared, and have the same coefficient, we know this is a circle.The goal is the form:(x - h)² + (y - k)² = r² ---> center is (h, k),circle w/center at (1,......
Hint( complete the square) when graphed what does it create.

Please explain how to get to the answer so I can learn myself. I don't even remember what (h,k) form is.

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Because x and y are both squared, and have the same coefficient, we know this is a circle. The goal is the form: (x - h)² + (y - k)² = r² ---> center is (h, k), radius is r

x² + y² - 2x + y + 1 = 0

(x² - 2x + _) + (y² + y + _) = -1
(x² - 2x + 1) + (y² + y + (1/4)) = -1 + 1 + (1/4)
(x - 1)² + (y + (1/2))² = 1/4

circle w/center at (1, (-1/2)), radius = 1/2

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x^2 + y^2 - 2x + y + 1 = 0

(x^2 - 2x + 1) + (y^2 + y +1/4) -1/4 = 0

factorize terms in brackets and add both sides by 1/4

(x -1)^2 + (y + 1/2)^2 = 1/4

This is the equation in (h,k) form where (x - h)^2 + (y - k)^2 = r^2 that graphs a circle with center (h,k) and a radius of r.
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