The equation of a right circular cone whose vertex is origin, axis z - axis and semivertical angle α is 

1
x2 + y2 = z2 sec2 α
2
z2 + x2 = y2 tan2 α 
3
x2 + y2 = z2 tan2 α
4
y2 + z2 = x2 tan2 α 

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