x2+y2−6x+8y=11

Question

What kind of graph is this?

Answer 1

x^2 + y^2 - 6x + 8y = 11

It should end up being a circle or ellipse.

x^2 - 6x + y^2 + 8y = 11

We want to make (x - 3)^2, but that has to have a +9 on the end, so we do this:

x^2 - 6x + 9 - 9 + y^2 + 8y = 11

(x - 3)^2 - 9 + y^2 + 8y = 11

Now we want to make (y + 4)^2, but that has to have a +16 on the end, so we do this:

(x - 3)^2 - 9 + y^2 + 8y + 16 - 16 = 11

(x - 3)^2 - 9 + (y + 4)^2 - 16 = 11

(x - 3)^2 + (y + 4)^2 - 25 = 11

(x - 3)^2 + (y + 4)^2 = 36

(x - 3)^2 + (y + 4)^2 = 6^2

Equation of a circle:  (x - a)^2 + (y - b)^2 = r2

Circle centered at (a,b) with radius r.

It's a circle centered at the point (3,-4) with a radius of 6.