Substitute the coordinates of A and B: 20+4d+2e+f = 0...②; 10-D+3E+F=0.........③;

Let x=0 in the formula (1), then there is y? +Ey+F = 0； Let the intercept of the garden on the y axis be y? ，y？ ; So y? +y？ =-E.......④;

Let y=0 in the formula (1), then there is x? +Dx+F = 0； Let the intercept of the garden on the x axis be x? ，x？ ; So x? +x？ =-D......⑤;

Known x? +x？ +y？ +y？ =-D-E = 2； That is e =-d-2; Substituting it into equation ②, we can get: 16+2D+F = 0...⑥.

And then substitute into formula ③, Simplifying: 4-4d+f = 0 ...................................................................................................................................................... ⑥-⑥:12+6d = 0, so d =-2; e = 0； f =- 12；

The equation of hometown is: x? +y？ -2x- 12 = 0； That is (x- 1)? +y？ = 13;