Answer:
( x - 2)^2 + ( y - 3)^2 = 34
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) - the center of the circle
( x, y) - any point on the circle
r^2 - radius of the circle
( -3 , 6) - point - ( x, y)
x = -3
y = 6
( 2 , 3) - center-( a, b)
a = 2
b = 3
Step 1: substitute the center into the equation
( x - 2)^2 + ( y - 3)^2 = r^2
Step 2: sub the point into the equation
( x - 2)^2 + ( y - 3)^2 = r^2
( -3 - 2)^2 + ( 6 - 3)^2 = r^2
( -5)^2 + 3^2 = r^2
25 + 9 = r^2
34 = r^2
Step 3: sub the radius into the equation
( x - 2)^2 + ( y - 3)^2 = r^2
( x - 2)^2 + ( y - 3)^2 = 34
Therefore, the equation of the circle is
( x - 2)^2 + ( y - 3)^2 = 34
