Eis the midpoint of df, de=2x+4, and ef=3x-1. find all segment lengths

If E is the midpoint, DE and EF are equivalent.
2x+4=3x-1
4=x-1
5=x

Plug the value of x in
2(5)+4
14

3(5)-1
14

14+14=28

Final DE=14, EF=14, DF= 28

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4