SOLUTION: The radius of a circle defined by x^2+y^2-2x-4y+1=0

Question 142614: The radius of a circle defined by x^2+y^2-2x-4y+1=0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The standard equation for a circle with radius and center at (,) is .

So, you have to complete the square for x and for y in your equation to put it into standard form. That way you can determine the radius directly.

Process:
Step 1: Rearrange the equation so that the constant is on the right and the variables are grouped on the left:

Step 2: Take the coefficient on the 1st degree x term, divide by 2 and square the result. Add that result to both sides of the equation.

so

Step 3: Repeat step 2 for the 1st degree y term.

so

Step 4: Factor the two trinomial parts of the left and collect terms on the right.

and , so:

Step 5: Take the square root of the resulting constant term to find the radius

Super-Double-Plus Extra Credit: Write the ordered pair that represents the center of this circle.

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