已知抛物线C:y=x2,从原点O出发且斜率为k0的直线l0交抛物线C于一异于O点的点A1(x1,y1),过A1作一斜率为

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  • An(xn,yn) An+1(xn+1,yn+1) yn=xn^2,yn+1=xn+1^2(An,An+1在抛物线上)

    xn+1^2-xn^2=(k0^n+1)(xn+1-xn) (直线方程) 化简:xn+1+xn=k0^n+1(因为An,An+1互异)

    xn+1=K0^n+1-xn(n≠0) x1=k0,x2=k0^2-k0+1,x3自己算

    xn=k0^(n-1)+1-(xn-1)=K0^(n-1)+1-K0^(n-2)-1+(Xn-2)=K0^(n-1)-K0^(n-2)+K0^(n-3)+1-(Xn-3)

    迭代:xn=K0^(n-1)-K0^(n-2)+K0^(n-3)...-K0+X1(n为奇数且n大于2)

    xn=K0^(n-1)-K0^(n-2)+K0^(n-3)...-K0+X1+1(n为偶数)