Question

How do you graph `x^2 + y^2 -6x + 2y - 6 = 0`?

Answer 1

Draw a circle with center `(3,-1)` and radius `4`.

Explanation:

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

`rarr color(red)(x^2-6x)+color(blue)(y^2+2y)=color(green)(6)`

`rarr color(red)(x^2-6x+9)+color(blue)(y^2+2y+1) = color(green)(6)color(red)(+9)color(blue)(+1)`

`rarr color(red)((x-3)^2) + color(blue)((y+1)^2) = color(orange)(4^2)`

which is the standard form for a circle with center `(3,-1)` and radius `4`.

graph{x^2-6x+y^2+2y-6=0 [-8.1, 9.68, -5.404, 3.48]}