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Mathematics
Problem
Prove that for a hyperbola with semi-transverse axis
a
a
a
and eccentricity
e
>
1
e>1
e
>
1
, the length of its semi-conjugate axis is
b
=
a
e
2
−
1
b=a\sqrt{e^{2}-1}
b
=
a
e
2
−
1
.
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