How to graph x 2 + y 2 - 4 x - 2 y - 4 = 0 ?

Question

How to graph             x      2        +          y      2        -    4    x    -    2    y    -    4    =    0  ?

popunjati7z8a · Accepted Answer

You can determine that the equation represents a circle from this form.
To find its coordinates and radius you should transform it to form of:

{(x - a)}^{2} + {(y - b)}^{2} = r^{2}

(1)
We start from the equation given:

x^{2} + y^{2} - 4 x - 2 y - 4 = 0

Now we can group terms with the same variable:

x^{2} - 4 x + y^{2} - 2 y - 4 = 0

Now we can complete the squares of variables:

x^{2} - 4 x + 4 + y^{2} - 2 y + 1 - 5 - 4 = 0

I added

5

so I had to substract 5 to keep the equation balanced.
Now we can write the expressions with

x

and

y

as squares:

{(x - 2)}^{2} + {(y - 1)}^{2} - 9 = 0

Finally I can move

9

to right side to get the form (1)

{(x - 2)}^{2} + {(y - 1)}^{2} = 9

From this equation I can read that the equation shows a circle with center in

C = (2; 1)

and radius

r = 3

How to graph x^2+y^2-4x-2y-4=0?