What does the equation (a-b)(x^2+Y^2)-2abx = 0 becomes if the origin is shifted to the point (ab/a-b, 0) without rotation?

Dear Chanchal,

Apply the concept of 'Parallal Transformation of Coordinate Axes'..As the origin has been shifted to (ab/a-b,0),so we can right x=ab/a-b+ab/a-b where the second ab/a-b=h{the distance of the new cordinate from the old one,here distance between (0,0) and (ab/a-b)}.Now put the value of x and solve..Most probably the equation would come out to be a line parallel to x-axis.

Goodluck and Warm Wishes,

Please approve the answer if it helped you.

initial coordinates of origin = (0,0)  &  the coordinates of general point = (X,Y)

final coordinates of origin = (ab/a-b,0) , & the coordinates of general point =(X¹,Y¹)

from here we can say

                     X¹ = X+ab/a-b     &  Y¹ = Y+0=Y

so keeping Y coordinate unchanged replace X by X+ab/a-b u will get the required equation....