a circle with center o is shown create the equation for the circle the point is at (1,1) the top touches 1,5 the left touches -3,1 assume the circle goes completely around the circle
To find the equation of a circle, you need the center coordinates (h, k) and the radius r.
Since the center of the circle is O and the point is at (1,1), the center of the circle is at (1,1).
The radius of the circle can be found by calculating the distance between the center and any point on the circle. We can take either the point (1,5) or (-3,1).
Let's calculate the radius using the point (-3,1):
r = √((x2 - x1)^2 + (y2 - y1)^2)
r = √((1 - (-3))^2 + (1 - 1)^2)
r = √((4)^2 + (0)^2)
r = √(16)
r = 4
Therefore, the equation of the circle with center at O(1,1) and passing through the point (1,5) and (-3,1) is:
(x-1)^2 + (y-1)^2 = 16