SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Complete the square and write the equation in standard form. Then give the center and radius of the circle. x^2 + y^2 - 2x - 4y -4

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Complete the square and write the equation in standard form. Then give the center and radius of the circle. x^2 + y^2 - 2x - 4y -4       Log On


   

Question 156163: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Complete the square and write the equation in standard form. Then give the center and radius of the circle. x^2 + y^2 - 2x - 4y -4 = 0.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+y%5E2+-+2x+-+4y+-4+=+0 Start with the given equation


x%5E2-+2x+%2B+y%5E2++-+4y+-4+=+0 Rearrange the terms (place the "x" and "y" terms together)


x%5E2-+2x+%2Bhighlight%281%29+%2B+y%5E2++-+4y+-4+=+highlight%281%29 Take half of the "x" coefficient and square it to get %28%28-2%29%2F2%29%5E2=%28-1%29%5E2=1. Add this to both sides (note: add the one right after the -2x)



x%5E2-+2x+%2B1+%2B+y%5E2++-+4y+%2Bhighlight%284%29+-4+=+1%2Bhighlight%284%29 Take half of the "y" coefficient and square it to get %28%28-4%29%2F2%29%5E2=%28-2%29%5E2=4. Add this to both sides (note: add the four right after the -4y)


x%5E2-+2x+%2B1+%2B+y%5E2++-+4y+%2B4+-4+=+5 Combine like terms on the right side

%28x%5E2-+2x+%2B1+%29%2B+%28y%5E2++-+4y+%2B4+%29-4+=+5 Group the terms into two groups of three terms in each


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


%28x-1%29%5E2%2B+%28y-2%29%5E2-4+=+5 Factor y%5E2++-+4y+%2B4 to get %28y-2%29%5E2


%28x-1%29%5E2%2B+%28y-2%29%5E2+=+9 Add 4 to both sides


Now we have an equation in the form of %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 where h=1, k=2, and r=3. Remember, for the general circle %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2, the center is (h,k) and and the radius is "r"


So for %28x-1%29%5E2%2B+%28y-2%29%5E2+=+9, the center is (1,2) and the radius is 3 units