Dễ dàng có `OA=2,OB=4/5`

`N in Δ=>N(t;-2t-2)`

Xét `ΔAOM` ta có:`(OB)/(OA)=(BN)/(AM)=>(BN)/(AM)=2/5=>5BN=2AM=>5\vec{BN}=2\vec{AM}`

`<=>{(5(x_N-x_B)=2(x_M-x_A)),(5(y_N-y_B)=2(y_M-y_A)):}`

`<=>{(x_M=(5(x_N-x_B)+2x_A)/2=5/2t),(y_M=(5(y_N-y_B)+2y_A)/2=-5t-5):}`

`=>M(5/2t;-5t-5)`

`M in d=>5/2t-(-5t-5)-1=0<=>t=-8/15`

Khi đó `M(-4/3;-7/3),N(-8/15;-14/15)`

Gọi PT đường tròn `(T)` là `x^2+y^2-2ax-2by+c=0(a^2+b^2-c>0)`

`(T)` đi qua `A,M,N`

`=>``{(0^2+2^2-2*a*0-2*b*2+c=0),((-4/3)^2+(-7/3)^2-2*a*(-4/3)-2*b*(-7/3)+c=0),((-8/15)^2+(-14/15)^2-2*a*(-8/15)-2*b*(-14/15)+c=0):}`

`<=>{(a=-245/36),(b=31/18),(c=26/9):}`

Khi đó `(T):x^2+y^2+245/18x-31/9y+26/9=0`

Vậy  `(T):x^2+y^2+245/18x-31/9y+26/9=0`