IB Mathematics Analysis and Approaches Quiz
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CALCULUS
Question 1
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The curve known as the lemniscate of Bernoulli is given by
(
x
2
+
y
2
)
2
=
2
(
x
2
−
y
2
)
(x^2 + y^2)^2 = 2(x^2 - y^2)
(
x
2
+
y
2
)
2
=
2
(
x
2
−
y
2
)
. Which of the following is an expression for
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in terms of
x
x
x
and
y
y
y
?
A
x
(
1
−
x
2
−
y
2
)
y
(
1
+
x
2
+
y
2
)
\frac{x(1 - x^2 - y^2)}{y(1 + x^2 + y^2)}
y
(
1
+
x
2
+
y
2
)
x
(
1
−
x
2
−
y
2
)
B
x
(
1
+
x
2
+
y
2
)
y
(
1
−
x
2
−
y
2
)
\frac{x(1 + x^2 + y^2)}{y(1 - x^2 - y^2)}
y
(
1
−
x
2
−
y
2
)
x
(
1
+
x
2
+
y
2
)
C
x
(
2
−
x
2
−
y
2
)
y
(
2
+
x
2
+
y
2
)
\frac{x(2 - x^2 - y^2)}{y(2 + x^2 + y^2)}
y
(
2
+
x
2
+
y
2
)
x
(
2
−
x
2
−
y
2
)
D
x
y
\frac{x}{y}
y
x
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