A slight change in notation should clear it up . . .
Find the equation of a line perpendicular to the ellipse , at the point (-1, 1).
The equation of the perpendicular line turned out to be: .
The question now is where does this line intersect the ellipse again?
We want the intersection of two curves: the ellipse and the line.
Substitute into: . . . . and solve.
We'll get two points . . . and we already know one of them . . . Got it?