<Dl> <Dd> F (x, y, z, a) = 0, F (x, y, z, a ′) − F (x, y, z, a) a ′ − a = 0 . (\ displaystyle F (x, y, z, a) = 0, \, \, (F (x, y, z, a ^ (\ prime)) - F (x, y, z, a) \ over a ^ (\ prime) - a) = 0 .) </Dd> </Dl> <Dd> F (x, y, z, a) = 0, F (x, y, z, a ′) − F (x, y, z, a) a ′ − a = 0 . (\ displaystyle F (x, y, z, a) = 0, \, \, (F (x, y, z, a ^ (\ prime)) - F (x, y, z, a) \ over a ^ (\ prime) - a) = 0 .) </Dd> <P> In the limit as a' approaches a, this curve tends to a curve contained in the surface at a </P> <Dl> <Dd> F (x, y, z, a) = 0, ∂ F ∂ a (x, y, z, a) = 0 . (\ displaystyle F (x, y, z, a) = 0, \, \, (\ partial F \ over \ partial a) (x, y, z, a) = 0 .) </Dd> </Dl>

Find the envelope of the family of curves