Question

What is the equation of the circle with center (-3,1) that passes through the point (-5, 3)?

Answer 1

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:

$(x-h)^2 + (y-k)^2 = r^2$

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:

$r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Given

$(x_1,y_1) = (-3,1)\\(x_2,y_2) = (-5,3)$

Putting the values in the formula

$r = \sqrt{(-5+3)^2+(3-1)^2}\\r = \sqrt{(-2)^2+(2)^2}\\r = \sqrt{4+4}\\r = \sqrt{8}$

Putting the values of h,k and r in general form of equation

$\{x-(-3)}^2\} +(y-1)^2 = (\sqrt{8})^2\\(x+3)^2+(y-1)^2 = 8$

Hence,

Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.