Determine the equation of the circle graphed below.
x
y
x
y
center (4, 6)
(7, 7)
To determine the equation of the circle, we need to use the formula for the standard form of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the radius.
In this case, the center is at (4, 6) and the point (7, 7) lies on the circle.
So, the radius can be calculated using the distance formula:
r = √((7 - 4)^2 + (7 - 6)^2)
r = √(3^2 + 1^2)
r = √(9 + 1)
r = √10
Therefore, the equation of the circle is:
(x - 4)^2 + (y - 6)^2 = 10