Question

Determine the equation of the circle graphed below.
x
y
x
y
(4, 3)
(7, 7)

Answer 1

To determine the equation of the circle graphed, we first need to find the center and radius of the circle using the given points (4, 3) and (7, 7).

The center of the circle can be found by taking the average of the x-coordinates and y-coordinates of the two given points:

Center = ((4 + 7) / 2, (3 + 7) / 2)
Center = (5.5, 5)

The radius of the circle can be found by calculating the distance between one of the points and the center:

Radius = sqrt((7 - 5.5)^2 + (7 - 5)^2)
Radius = sqrt((1.5)^2 + (2)^2)
Radius = sqrt(2.25 + 4)
Radius = sqrt(6.25)
Radius = 2.5

Therefore, the equation of the circle with center (5.5, 5) and radius 2.5 is:

(x - 5.5)^2 + (y - 5)^2 = 2.5^2
(x - 5.5)^2 + (y - 5)^2 = 6.25