Completing the squares, the equation of the circle is and the graph is given at the end of the answer.
What is the equation of a circle?
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
For this problem, the equation is:
x² + y² + 6x - 4y - 12 = 0.
We have to complete the squares to place the equation of the circle in standard format, hence:
x² + 6x + y² - 4y = 12.
(x + 3)² + (y - 2)² = 12 + 3² + 2²
(x + 3)² + (y - 2)² = 25.
Which means that we have a circle that:
The graph is sketched at the end of this answer.
More can be learned about the equation of a circle at https://brainly.com/question/24307696
#SPJ1
