Let's analyze and solve the given equations to find the requested properties.

Problem 4:

Equation:
$x^2 + y^2 - 6x + 2y + 9 = 0$

1. Complete the square for $x$- and $y$-terms to convert the equation into standard form:

$(x^2 - 6x) + (y^2 + 2y) = -9$

Completing the square: [ (x - 3)^2 - 9 + (y + 1)^2