This is a question from my practice test I am trying to stud

This is a question from my practice test, I am trying to study for my test next week, so if you can explain how to get the answer and show the steps on the calculator. Thank you.

18. Suppose that the equation of the circle is given by c2 y +2z +6y +9 0. Which of the following graphs is the graph of the circle? (b) (e) (d)

Solution

Given equation of circle is

x^2 + y^2 + 2x + 6y + 9 = 0

by making the complete squares, equation becomes

(x + 1)^2 + (y + 3)^2 = 1

where center of circle is (-1, -3) and radius is 1 unit.

The correct graph is graph (a)