Standard Form of Equation of Circle

42. We can use the 2 points to find the midpoint (center of the circle):
midpoint is (2, 2)
The radius is the distance from (2,2) to (0,1)
d=sqrt(2^2+(2-1)^2)=sqrt(4+1)=sqrt(5)
Equation: (x-2)^2+(y-2)^2=5

Implosive constipation.

44. (h-k)^2+(y-k)^2=r^2
(h,k) is (4,-2)
As the circle is tangent to x=1, one of the points on the circle will have an x-coordinate of 1
The point is (4,1)
We can use the distance formula to find the radius
d=sqrt((4-4)^2+(2-(-1))^2)=sqrt(9)=3
Equation: (x-4)^2+(y+2)^2=9