Answer:
[tex](x + 4)^{2} + (y + 1)^{2} = 29[/tex].
Step-by-step explanation:
The equation of a circle of radius [tex]r[/tex] and center [tex](a,\, b)[/tex] is:
[tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex].
In this question, it is given that the center is [tex](-4,\, -1)[/tex], such that [tex]a = (-4)[/tex] while [tex]b = (-1)[/tex].
The radius of this circle could be found as the distance between the center of this circle, [tex](-4,\, -1)[/tex], and any point on the circle- such as [tex](1,\, -3)[/tex]. Using the distance formula, the radius of this circle would be:
[tex]\begin{aligned}r &= \sqrt{((-4) - 1)^{2} + ((-1) - (-3))^{2}} \\ &= \sqrt{29}\end{aligned}[/tex].
Therefore, the equation of this circle would be:
[tex](x - (-4))^{2} + (y - (-1))^{2} = (\sqrt{29})^{2}[/tex].
Simplify to obtain:
[tex](x + 4)^{2} + (y + 1)^{2} = 29[/tex].
