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Mathematics
Problem
A circle cuts the rectangular hyperbola
x
y
=
1
xy = 1
x
y
=
1
in points
(
x
r
,
y
r
)
(x_r, y_r)
(
x
r
,
y
r
)
,
r
=
1
,
2
,
3
,
4
r = 1, 2, 3, 4
r
=
1
,
2
,
3
,
4
then prove that
x
1
x
2
x
3
x
4
=
y
1
y
2
y
3
y
4
=
1
x_1x_2x_3x_4 = y_1y_2y_3y_4 = 1
x
1
x
2
x
3
x
4
=
y
1
y
2
y
3
y
4
=
1
.
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