Answer:
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the center (-2, 1) → h = -2 and k = 1.
The radius is the distance between the center and the given point.
Therefore put the coordinates of the points (-2, 1) and (-4, 1) to the formula of a distance between two points:
[tex]r=\sqrt{(-4-(-2))^2+(1-1)^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2[/tex]
We have the equation in standard form:
[tex](x-(-2))^2+(y-1)^2=2^2\\\\(x+2)^2+(y-1)^2=4[/tex]
Convert to the genereal form using:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\\\\x^2+y^2+4x-2y+5=4\qquad\text{subtract 4 from both sides}\\\\\boxed{x^2+y^2+4x-2y+1=0}\to\boxed{B.}[/tex]
