A curve has equation

3x² – 4xy + 2y² – 2 = 0

(i) Show that

(ii) Find the exact coordinates of the points on the curve where the tangent is parallel to the x-axis.

(iii) The normal of the curve at the point *P* with coordinates (0,1), meets the curve again at point *Q*. Find the area of triangle *OPQ*, where *O* is the origin.