Find the equation of the hyperboloid of one sheet passing through the points (plus and minus 7,0,0), (0,plus and minus 2,0) and (plus and minus 14,0,6), (0, plus and minus 4, 6)
1 Answer

x²/a² + y²/b² – z²/c² = 1
“passing through the point (±7, 0, 0)”
49/a² = 1
a² = 49
“passing through the point (0, ±2, 0)”
4/b² = 1
b² = 4
“passing through the point (±14, 0, 6)”
196/a² – 36/c² = 1
196/49 – 36/c² = 1
c² = 12
“passing through the point (0, ±4, 6)”
This is too much information, but fortunately not in contradiction with previous information (16/b²36/c²=1 => c²=12).
The equation of the hyperboloid is
x²/49 + y²/4 – z²/12 = 1
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