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Mathematics
Problem
The point on the curve
x
2
y
+
y
2
=
9
x^{2}y+y^{2}=9
x
2
y
+
y
2
=
9
with
x
=
1
x=1
x
=
1
and positive
y
y
y
–coordinate is
(
1
,
−
1
+
37
2
)
\Bigl(1,\tfrac{-1+\sqrt{37}}{2}\Bigr)
(
1
,
2
−
1
+
37
)
. What is the slope of the tangent line to the curve at that point? a)
37
−
1
37
\dfrac{\sqrt{37}-1}{\sqrt{37}}
37
37
−
1
b)
−
1
-1
−
1
c)
1
37
−
1
\dfrac{1}{\sqrt{37}}-1
37
1
−
1
d)
1
−
37
2
37
\dfrac{1-\sqrt{37}}{2\sqrt{37}}
2
37
1
−
37
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