Answer:
( x + 3)^2 + ( y - 1)^2 = 8
Step-by-step explanation:
The equation of a circle with a center and a point
( x - a) ^2 + ( y - b) ^2 = r^2
( x , y) - any point on the circle
( a, b) - center of the circle
r^2 - radius of the circle
( -3 , 1) - center - ( a, b)
a = -3
b = 1
( -5 , 3) - point - ( x, y)
x = -5
y = 3
Step 1: substitute the center into the equation
( x -(-3)^2 + ( y - 1)^2 = r^2
( x + 3)^2 + ( y - 1)^2 = r^2
Step 2 : sub the point into the equation
( x + 3)^2 + ( y - 1)^2 = r^2
( -5 + 3)^2 + ( 3 - 1)^2 = r^2
(-2)^2 + 2^2 = r^2
4 + 4 = r^2
8 = r^2
Step 3 : sub the radius into the equation
( x + 3)^2 + ( y - 1)^2 = r^2
( x + 3)^2 + (y - 1)^2 = 8
Therefore, the equation of the circle is
( x + 3)^2 + (y - 1)^2 = 8
![2^{1/3} = \sqrt[3]{2}](https://tex.z-dn.net/?f=2%5E%7B1%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7B2%7D)