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Mathematics
Mathematics
Problem
Consider the family of curves given by
x
y
+
p
y
2
+
q
x
=
1
x y + p y^{2} + q x = 1
x
y
+
p
y
2
+
q
x
=
1
, where
p
p
p
and
q
q
q
are real constants. For the point
(
1
,
1
)
(1,1)
(
1
,
1
)
on such a curve, which ordered pair
(
p
,
q
)
(p,q)
(
p
,
q
)
yields a horizontal tangent at that point? a)
(
−
1
2
,
1
2
)
\left(-\dfrac12,\dfrac12\right)
(
−
2
1
,
2
1
)
b)
(
−
1
,
1
)
(-1,1)
(
−
1
,
1
)
c)
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
d)
(
2
,
−
1
)
(2,-1)
(
2
,
−
1
)
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