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Figure Eight Curve
Cartesian equation:
x
4
=
a
2
(
x
2
−
y
2
)
x^{4} = a^{2}(x^{2}-y^{2})
x
4
=
a
2
(
x
2
−
y
2
)
Polar equation:
r
2
=
a
2
cos
(
2
θ
)
sec
4
(
θ
)
r^{2} = a^{2}\cos(2 \theta )\sec^{4}( \theta )
r
2
=
a
2
cos
(
2
θ
)
sec
4
(
θ
)
View the interactive version of this curve.
Description
This curve is also known as the
Lemniscate of Gerono
.
Other Web site:
Xah Lee
Associated Curves
Definitions of the Associated curves
Evolute
Involute 1
Involute 2
Inverse curve wrt origin
Inverse wrt another circle
Pedal curve wrt origin
Pedal wrt another point
Negative pedal curve wrt origin
Negative pedal wrt another point
Caustic wrt horizontal rays
Caustic curve wrt another point
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