Answer:
( x + 1)^2 + ( y - 3)^2 = 25
Step-by-step explanation:
The equation of the 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
( -1 , 3) - ( center) - ( a, b)
a = -1
b = 3
( 3 , 6) - ( point) - ( x, y)
x = 3
y = 6
Step 1: substitute the center 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
( 3 + 1)^2 + ( 6 - 3)^2 = r^2
4^2 + 3^2 = r^2
16 + 9 = r^2
25 = r^2
Step 3: sub the radius into the equation
( x + 1)^2 + ( y - 3)^2 = r^2
( x + 1)^2 + (y - 3)^2 = 25
Therefore, the equation of the circle is
( x + 1)^2 + (y - 3)^2 = 25
