Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 214
FP = m2. Hence [0 - c)2 + f] [O + c)2 + y2] = m4, or (a? + y2 + c2)2 - 4 c2x2=m* is the equation of the Cassinian oval. The intercepts of the curve on the axes are ± Vc2 ± m2and ± Vm2 — c2. Hence if c<m, the curve cuts each axisin two real points and has the form shown in Fig. 99.While if… … Fig. 100. goes through the origin. In this case the equation re-duces to x2 + y2 = 2 c2(x> - y2), or in polar coordinates, p2=2c2 cos 2 6. This special form of the Cassinian oval is called thelemniscate. It has already been discussed on page 67. 198 ANALYTIC GEOMETRY [Ch. XV, § 103 103. The…
Geometry, Analytic
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