Question 1124951
your diameter goes between the points (2,-2) and (1,5)


the distance between those 2 points is sqrt((x2-x1)^2 + (y2-y1)^2)


let (2,-2)  = (x1,y1) and let (1,5) = (x2,y2).


the distance between those two points becomes equal to sqrt((1-2)^2 + (5--2)^2)


that becomes sqrt(-1^2 + 7^2) = sqrt(50)


that's the length of the diameter.


the length of the radius is half that, so the length of the radius is sqrt(50) / 2.


the center of the circle is the midpoint of the diameter.


the formula for that is (x1 + x2) / 2, (y1 + y2) / 2)


since (2,-2)  = (x1,y1) and (1,5) = (x2,y2), the midpoint formula becomes:


((2+1)/2,(-2+5)/2) = (3/2,3/2)


that's the center of the circle, therefore (h,k) = (3/2,3/2).


r = sqrt(50)/2 which makes r^2 = 50/4 = 12.5


the formuls of the circle is (x-h)^2+(y-k)^2=r^2


that becomes (x - 3/2)^2 + (y - 3/2)^2 = 12.5


here's the graph of that equation.


<img src = "http://theo.x10hosting.com/2018/100105.jpg" alt="$$$" >


the blue line is the line that contains the diameter of the circle.


the circle itself is also in blue.


the orange lines are only there to allow the intersections to be shown.