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Mathematics
Problem
The equation of the chord joining two points
(
x
1
,
y
1
)
(x_1, y_1)
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
(x_2, y_2)
(
x
2
,
y
2
)
on the rectangular hyperbola
x
y
=
c
2
xy = c^2
x
y
=
c
2
is a.
x
x
1
+
x
2
+
y
y
1
+
y
2
=
1
\frac{x}{x_1 + x_2} + \frac{y}{y_1 + y_2} = 1
x
1
+
x
2
x
+
y
1
+
y
2
y
=
1
b.
x
x
1
−
x
2
+
y
y
1
−
y
2
=
1
\frac{x}{x_1 - x_2} + \frac{y}{y_1 - y_2} = 1
x
1
−
x
2
x
+
y
1
−
y
2
y
=
1
c.
x
y
1
+
y
2
+
y
x
1
+
x
2
=
1
\frac{x}{y_1 + y_2} + \frac{y}{x_1 + x_2} = 1
y
1
+
y
2
x
+
x
1
+
x
2
y
=
1
d.
x
y
1
−
y
2
+
y
x
1
−
x
2
=
1
\frac{x}{y_1 - y_2} + \frac{y}{x_1 - x_2} = 1
y
1
−
y
2
x
+
x
1
−
x
2
y
=
1
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