Mathematics Parabola, Ellipse and Hyperbola Applications of Conics

Find the equation of the cone with vertex at the origin and direction cosines of its generators satisfy the equation l2 + 2m2 - 3n2 = 0

1
x2 + y2 - z2 = 0
2
x2 + 2y2 - 3z2 = 0
3
x2 - 2y2 + 3z2 = 0
4
xy + yz + zx = 0

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