Question: Show that the surface x 2 - 2yz + y 3 = 4 is (perpendicular) to any member of the family of surfaces x 2

Show that the surface x2 - 2yz + y3 = 4 is (perpendicular) to any member of the family of surfaces x2 + 1 = (2 - 4a)y2 + az2 at the point of intersection (1, -1, 2).

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