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(D) The general equation of a circle is $x^{2}+y^{2}+2gx+2fy+c=0$,with center $(-g, -f)$.For the first circle $x^{2}+y^{2}+2x-4y+1=0$,the center $A$ i

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$x^{2}+y^{2}-3x+y-10=0$

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(D) The general equation of a circle is $x^{2}+y^{2}+2gx+2fy+c=0$,with center $(-g, -f)$.For the first circle $x^{2}+y^{2}+2x-4y+1=0$,the center $A$ is $(-1, 2)$.For the second circle $x^{2}+y^{2}-8x+6y+17=0$,the center $B$ is $(4, -3)$.The equation of a circle with diameter endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $(x-x_{1})(x-x_{2})+(y-y_{1})(y-y_{2})=0$.Substituting the coordinates of $A$ and $B$:$(x-(-1))(x-4)+(y-2)(y-(-3))=0$$(x+1)(x-4)+(y-2)(y+3)=0$$x^{2}-4x+x-4+y^{2}+3y-2y-6=0$$x^{2}+y^{2}-3x+y-10=0$.

The equation of the circle whose end points of a diameter are the centres of the circles $x^{2}+y^{2}+2x-4y+1=0$ and $x^{2}+y^{2}-8x+6y+17=0$ is

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