Answer:
( x + 1)^2 + (y - 3)^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
( a , b) - center of the circle
( x, y) - any point on the circle
r^2 - radius of the circle
We are provided with a center and a point
( -1 , 3) - ( a, b) - center
a = -1
b = 3
( 1 , 1) - ( x, y) - point
x = 1
y = 1
Step1: substitute the center of the circle into the equation
( x - (-1)^2 + ( y - 3)^2 = r^2
(x + 1)^2 + (y - 3)^2 = r^2
Step 2: sub the point into the equation
( x + 1)^2 + (y - 3)^2 = r^2
x - 1
y - 1
( 1 + 1)^2 + ( 1 - 3)^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 + 1)^2 + ( y - 3)^2 = r^2
( x + 1)^2 + (y - 3 )^2 = 8
Therefore, the equation of the circle is
( x + 1)^2 + ( y - 3)^2 = 8
