The locus of the centre of the circle passing through the intersection of the circles x^2+y^2=1 and x^2+y^2-2x+y=0 is?

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Please find the answer to your question below
GIven equations of circles are
x^2+y^2=1 and x^2+y^2-2x+y=0
So by taking a constantand writing the equation as
x^2+y^2-1+(x^2+y^2-2x+y)=0
As given to find out the locus of center of circle we can get its value by substitution of the center
And the locus of intersection is a line with equation as x-2y=0