The hyperbolic lemniscate has for its equation (x2 +y2)2 = a2x2 - b 2 y 2 or r 2 =a 2 cos 2 0 - b 2 sin 2 B.
The same name is also given to the first positive pedal of any central conic. When the conic is a rectangular hyperbola, the curve is the lemniscate of Bernoulli previously described.
The elliptic lemniscate has for its equation (x 2 +31 2) 2 =a 2 x 2 +b 2 y 2 or r 2 = a 2 cos 2 9 +b 2 sin 20 (a> b).
LEMNISCATE (from Gr.
The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.