Answer:
( x - 14)^2 + ( y - 9)^2 = 13
Step-by-step explanation:
The equation of the circle with a center and a point
( x - a) ^2 + ( y - b) ^2 = r^2
( 14 , 9) - center-( a, b)
a = 14
b = 9
( 16 , 12) - point - ( x, y)
x = 16
y = 12
Step 1: substitute the center into the equation
( x - 14)^2 + ( y - 9)^2 = r^2
Step 2: substitute the point into the equation
( x - 14)^2 +( y - 9)^2 = r^2
( 16 - 14)^2 + ( 12 - 9)^2 = r^2
2^2 + 3^2 = r^2
4 + 9 = r^2
13 = r^2
Step 3: subs the radius into the equation
( x - 14)^2 + ( y - 9)^2 = r^2
( x - 14)^2 + (y - 9)^2 = 13
Therefore, the equation of the circle is
( x - 14)^2 + ( y - 9)^2 = 13
