Answer:
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.
Step-by-step explanation:
The equation of a circle with center (h,k) and radius r is given by:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Given
Center = (h,k) = (-3,1)
=> h = -3
=> k = 1
The distance between the center of circle and the point through which the circle passes will be the radius.
The distance formula is given by:
[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Given
[tex](x_1,y_1) = (-3,1)\\(x_2,y_2) = (-5,3)[/tex]
Putting the values in the formula
[tex]r = \sqrt{(-5+3)^2+(3-1)^2}\\r = \sqrt{(-2)^2+(2)^2}\\r = \sqrt{4+4}\\r = \sqrt{8}[/tex]
Putting the values of h,k and r in general form of equation
[tex]\{x-(-3)}^2\} +(y-1)^2 = (\sqrt{8})^2\\(x+3)^2+(y-1)^2 = 8[/tex]
Hence,
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.
