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Mathematics
Problem
Consider the family of curves defined by
x
2
+
k
x
y
+
y
2
=
1
x^{2}+kxy+y^{2}=1
x
2
+
k
x
y
+
y
2
=
1
, where
k
k
k
is a constant parameter. Which of the following gives
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
expressed in terms of
x
x
x
,
y
y
y
, and
k
k
k
? a)
2
x
+
k
y
k
x
+
2
y
\dfrac{2x+ky}{kx+2y}
k
x
+
2
y
2
x
+
k
y
b)
−
2
x
+
k
y
k
x
+
2
y
-\dfrac{2x+ky}{kx+2y}
−
k
x
+
2
y
2
x
+
k
y
c)
−
k
x
+
2
y
2
x
+
k
y
-\dfrac{kx+2y}{2x+ky}
−
2
x
+
k
y
k
x
+
2
y
d)
−
2
x
+
k
y
2
y
-\dfrac{2x+ky}{2y}
−
2
y
2
x
+
k
y
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