Algebraic circle equation, conversion to standard form?

Question

I've this problem (copied exactly) for homework:

"Rewrite the equation of the circle x2 + y2 – x + 2y + 1 = 0 into standard form, and identify the coordinates of the center and radius."

I assume that the 2s following the variables indicate a squared value, but the teacher must've forgotten a caret or to use superscript (superscript appears earlier in the homework document, but not here. Go figure).

I know standard form; ((x-h)^2 + (y-k)^2) = r^2

However, I can only get so far as rearranging the terms to:

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

I know at this point I need to 'complete the square', so that I can move the exponent to the outside of the parentheses...

All I really need is help to figure out what to do with regard to the -x term. I can't really multiply a term by two to get -1...

Could there be another way of writing the standard form that I don't know of? I dunno...

Any response is gladly appreciated~!

Answer 1

You CAN multiply a term by 2 to get -1.  Think fractions here....

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

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

Center (1/2,-1) radius 1/2

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