Answer:
the equation of the circle is:
(x - 5)^2 + (y - 5)^2 = 13
Explanation:
To find the equation of a circle given two points where a line intersects it, we need to first find the center and radius of the circle. We can do this by finding the midpoint of the line segment connecting the two intersection points, which is the center of the circle, and the distance between the center and one of the intersection points, which is the radius of the circle.
The midpoint of the line segment connecting (2, 3) and (8, 7) is: ((2+8)/2, (3+7)/2) = (5, 5)
So the center of the circle is (5, 5).
The radius of the circle is the distance between the center (5, 5) and one of the intersection points, say (2, 3). We can use the distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2)
where (x1, y1) = (2, 3) and (x2, y2) = (5, 5).
So the radius of the circle is: d = sqrt((5-2)^2 + (5-3)^2) = sqrt(9 + 4) = sqrt(13)