The form is
(x - h)^2 + ( y - k)^2 = radius^2 where (h, k) is the center.....so....
( x + 1)^2 + ( y - 7)^2 = 10^2
(x + 1)^2 + ( y - 7)^2 = 100
Second one
The center is found by the mid-point formula
( [2 - 4]/ 2 , [7 + 4] / 2 ) = ( -1, 11/2)
The radius can be found by taking (1/2) of the diameter...so
(1/2) sqrt [ ( -4 - 2)^2 + ( 7 - 4)^2 ] = (1/2) sqrt [ (- 6)^2 + 3^2 ) = (1/2) sqrt (45)
r^2 = 45 / 4
So....the equation is
( x + 1)^2 + ( y - 11/2)^2 = 45 / 4
Here's a graph : https://www.desmos.com/calculator/walfxegecn