Editing Lemniscate of Bernoulli (section)

==Further properties==
[[File:Lemniskate hyperbel.svg|thumb|upright=1.25|The inversion of hyperbola yields a lemniscate]]
*The lemniscate is symmetric to the line connecting its foci {{math|''F''<sub>1</sub>}} and {{math|''F''<sub>2</sub>}} and as well to the perpendicular bisector of the line segment {{math|''F''<sub>1</sub>''F''<sub>2</sub>}}.
*The lemniscate is symmetric to the midpoint of the line segment {{math|''F''<sub>1</sub>''F''<sub>2</sub>}}.
*The area enclosed by the lemniscate is {{math|''a''<sup>2</sup> {{=}} 2''c''<sup>2</sup>}}.
*The lemniscate is the [[Inversive_geometry#Circle_inversion|circle inversion]] of a [[hyperbola]] and vice versa.
*The two tangents at the midpoint {{math|''O''}} are perpendicular, and each of them forms an angle of {{math|{{sfrac|{{pi}}|4}}}} with the line connecting {{math|''F''<sub>1</sub>}} and {{math|''F''<sub>2</sub>}}.
*The planar cross-section of a standard [[torus]] tangent to its inner equator is a lemniscate.
*The [[curvature]] at <math>(x,y)</math> is <math>{3\over a^2}\sqrt{x^2+y^2}</math>. The maximum curvature, which occurs at <math>(\pm a,0)</math>, is therefore <math>3/a</math>.