Question

Graph the circle x2 + y2 - 12x + 6y +36 =0​

Answer 1

x^2+y^2-12x+6y+36=0

Top Point: (6,0)

Left Point: (3,-3)

Right Point: (9,-3)

Bottom Point: (6,-6)

Answer 2

`x^2 +y^2 -12x +6y +36 =0`

And we can complete the squares like this:

`(x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2`

And we got:

`(x-6)^2 + (y+3)^2 = 9`

And we have a circle with radius r =3 and the vertex would be;

`V= (6,-3)`

The graph is on the figure attached.

Explanation:

For this case we have the following expression:

`x^2 +y^2 -12x +6y +36 =0`

And we can complete the squares like this:

`(x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2`

And we got:

`(x-6)^2 + (y+3)^2 = 9`

And we have a circle with radius r =3 and the vertex would be;

`V= (6,-3)`

The graph is on the figure attached.