A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z - 4y2 = 36 is given by the vector equation : r (t) = 6cosh(t) i + 2sinh(t) j + (36 - 16 sin2(t) ) K ,O st s 2n r (t) = 6cos(t) i + 2sin(t) j + (36 - 16 sin2(t) ) K ,O sts 2n r (t) = cos(t) i + sin(t) j + (36 - 16 sin2(t) ) K ,0 st s 2n r (t) = 6cos(t) i + 6sin(t) j + 36(1 + 4 sin2(t) ) k , 0 s t < 2n r (t) = cos(t) i + 3sin(t) j + 36cos2(t) k , 0

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