(x+y)=k(x-y)
=> (x+y)^2 = k(x-y)(x+y)
=> x^2+y^2+2xy = k(x^2-y^2)
=> x^2+y^2 = k(x^2-y^2)-2xy
Is it none of the above.
geometric approach :
(x+y) = k(x-y)
here, x+y is line 1 and x-y is line 2.
These who are equated hence they have same distance from the origion.
slope of line 1 : 1/1 = 1
slope of line 2 : -1/1 = -1
slope1*slope2 = -1
hence these two lines are perpendicular.
x^2+y^2 is the perpendicular distance from and of these two lines which is neither dependent om x^2-y^2 and xy.
so, Is it none of the above.