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Mathematics
Problem
Let
H
1
H_{1}
H
1
be the hyperbola
x
2
3
−
y
2
2
=
1
\frac{x^{2}}{3} - \frac{y^{2}}{2} = 1
3
x
2
−
2
y
2
=
1
and
H
2
H_{2}
H
2
be its conjugate hyperbola. Let
d
1
d_{1}
d
1
be the distance between the directrices of
H
1
H_{1}
H
1
and
d
2
d_{2}
d
2
be the distance between the directrices of
H
2
H_{2}
H
2
. Calculate the value of
5
(
d
1
2
+
d
2
2
)
5(d_{1}^{2} + d_{2}^{2})
5
(
d
1
2
+
d
2
2
)
.
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