SOLUTION: Complete the square and write the equation in standard form. Then give the center and radius of the circle. x2 + y2 - 2x - 4y - 4 = 0

Algebra ->  Human-and-algebraic-language -> SOLUTION: Complete the square and write the equation in standard form. Then give the center and radius of the circle. x2 + y2 - 2x - 4y - 4 = 0       Log On


   

Question 152653: Complete the square and write the equation in standard form. Then give the center and radius of the circle.
x2 + y2 - 2x - 4y - 4 = 0

Answer by mducky2(62) About Me  (Show Source):
You can put this solution on YOUR website!
It's easier to start by separating the x's from the y's:
x%5E2+%2B+y%5E2+-+2x+-+4y+-+4+=+0
%28x%5E2+-+2x%29+%2B+%28y%5E2+-+4y%29+-+4+=+0

In order to complete the square, we can use this equation:
x%5E2+%2B+bx+%2B+%28b%2F2%29%5E2+=+%28x+%2B+b%2F2%29%5E2

Now let's make the x's fit into this equation:
x%5E2+-+2x
We know that b = -2. But make sure to subtract whatever you add on so that everything adds up back in the original formula:
x%5E2+-+2x+%2B+1%5E2+-+1%5E2
x%5E2+-+2x+%2B+1+-+1
%28x+%2B+1%29%5E2+-+1

Now let's make the y's fit into this equation:
y%5E2+-+4y
We know that b = -4
y%5E2+-+4y+%2B+2%5E2+-+2%5E2
y%5E2+-+4y+%2B+4+-+4
%28y+-+4%29%5E2+-+4

Putting everything back into the original equation, we can now write it in standard form:
%28x%5E2+-+2x%29+%2B+%28y%5E2+-+4y%29+-+4+=+0
%28%28x+%2B+1%29%5E2+-+1%29+%2B+%28%28y+-+4%29%5E2+-+4%29+-+4+=+0

Moving all the excess numbers to the side:
%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+-+4+-+1+-+4+=+0
%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+-+9+=+0
%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+=+9

The center of a circle (h,k) and the radius r can be found using this equation:
%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2

Back to the equation:
%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+=+9
It looks like h = -1 and k = 4. Therefore the center of the circle is (-1,4).

It also looks like r2 = 9. Let's solve for r:
r%5E2+=+9
r+=+3
Therefore, the radius of the circle is 3.