Parabola Inverse Curve
The inverse curve for a parabola given by
with inversion center 👁 (x_0,y_0)
and inversion radius 👁 k
is
| 👁 x | 👁 = | 👁 x_0+(k(at^2-x_0))/((at^2+x_0)^2+(2at-y_0)^2) |
(3)
|
| 👁 y | 👁 = | 👁 y_0+(k(2at-y_0))/((at^2+x_0)^2+(2at-y_0)^2). |
(4)
|
For 👁 (x_0,y_0)=(0,0)
at the parabola vertex, the inverse
curve is the cissoid of Diocles
For 👁 (x_0,y_0)=(a,0)
at the focus, the inverse
curve is the cardioid
See also
Inverse Curve, Inversion, ParabolaExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Parabola Inverse Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParabolaInverseCurve.html