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Mathematics
Mathematics
Problem
Consider the curve defined by
x
y
+
p
x
+
q
y
=
1
xy + px + qy = 1
x
y
+
p
x
+
q
y
=
1
, where
p
p
p
and
q
q
q
are constants. Determine the values of
p
p
p
and
q
q
q
such that the curve passes through
(
1
,
2
)
(1,2)
(
1
,
2
)
and the tangent line there has slope
5
5
5
.
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