Let (x1, y1) be the pole of line lx + my + n = 0.     ...... (1)

w.r.t. the ellipse x^2/a^2 + y^2/b^2 = 1                     ...... (2)

Now the polar of (x^1, y^1) w.r.t. (2) is x*x1/a^2 + y*y1/b^2 = 1               ...... (3)

Since (1) and (3) represents the same polar, so comparing them we have

(x1/a2)/l + (y1/b2)/b2 = (-1)/n

or    x1 = ((-a^2)*l) /n   and    y1 = ((-b^2)*m) /n

.·. The required pole is ( ((-a^2)*l)/n , ((-b^2)*m)/n )