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Mathematics
Mathematics
Problem
Prove that the locus of the middle-points of the chords of the hyperbola
x
2
a
2
−
y
2
b
2
=
1
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
a
2
x
2
−
b
2
y
2
=
1
which pass through a fixed point
(
α
,
β
)
(\alpha, \beta)
(
α
,
β
)
is a hyperbola whose centre is
(
α
2
,
β
2
)
\left(\frac{\alpha}{2}, \frac{\beta}{2}\right)
(
2
α
,
2
β
)
.
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