If the origin is shifted to the point aba-b, 0 without rotation, then the equation (a−b)(x2+y2)−2abx=0becomes

The given equation is (a−b)(x2+y2)−2abx=0 ……(1)The origin is shifted to (ab/(a-b),0). Any point (x.y) on the curve (1) must be replaced with a new point (X,Y) with reference to the new axes, such that x=X+aba−b and y=Y+0Substituting these in (i), we get (a−b)[(X+aba−b)2+Y2]−2ab[X+aba−b]=0or (a−b)[(X2+a2b2(a−b)2)2+Y2+2abXa−b]−2abX−2a2b2a−b=0or (a−b)(X2+Y2)=a2b2a−b or (a−b)(X2+Y2)=a2b2