The equation represents the general form a circle with a center at
(–2, –3) and a diameter of 8 units is,
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
Given that,circle with a center at (–2, –3)
diameter of circle is 8 units
To find
the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the Circle is,
The diameter of the circle is 8 units. therefore,
[tex]radius=\frac{d}{2}=\frac{8}{2} =4[/tex]
Equation of a circle
The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units.
[tex](x-h)^{2} +(y-k)^{2} =R^{2}[/tex]
Substituting the values,
[tex](x-(-2))^{2} + (y-(-3))^{2} =4^{2}[/tex]
[tex](x+2)^{2} + (y+3)^{2} =4^{2}\\[/tex]
[tex]x^{2} +4x+4+y^{2} +6y+9=0[/tex]
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
Therefore, the option C is correct.
The equation represents the general form a circle with a center at
(–2, –3) and a diameter of 8 units is
[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]
To learn more about the general form of circle visit:
https://brainly.com/question/3612143
