about to only mathematics

Explanation

Given, `(x+2)^(2) + (y-3)^(2)=4`
let the coordinates be M (h,k), where B is mid-point of A and M.
`rArr B((h)/(2),(k+3)/(2))`
But AB is the chord of circle
`x^(2)+4x+(y-3)^(2)=0`
Thus, B must satisfy above equation.
`therefore (h^(2))/(4)+(4h)/(2)+[(1)/(2)(k+3)-3]^(2)=0`
`rArr h^(2)+k^(2)+8h-6k+9=0`
`therefore` Locus of M is the circle
`x^(2) +y^(2)+8x-6y+9=0`