your equation describes an ellipse with its centre in the origin.
At (1,2) the tangent to the ellipse has the slope zero, thus the normal line is a parallel to the y-axis. The other point which you were looking for has the same x-value as the given point. Plug in x = 1 into your equation and solve for y. You'll get y = 2 (that's the given point) or y = -1.
So the unknown point is (1, -1).