The equation for the given circle is:
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
How to get the equation of the circle?
Remember that for a circle whose center is (a, b) and has a radius r, the equation is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.
Then the equation is:
[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]
Expanding the squares we get:
[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
So the correct option is the third one.
If you want to learn more about circles:
https://brainly.com/question/1559324
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