卡西尼卵形线

${\displaystyle {\mbox{dist}}(q_{1},p){\mbox{dist}}(q_{2},p)=b^{2}\,}$

q1q2称为卵形线的焦点

${\displaystyle ((x-a)^{2}+y^{2})((x+a)^{2}+y^{2})=b^{4}}$

${\displaystyle (x^{2}+y^{2})^{2}-2a^{2}(x^{2}-y^{2})+a^{4}=b^{4}}$

${\displaystyle (x^{2}+y^{2}+a^{2})^{2}-4a^{2}x^{2}=b^{4}}$

${\displaystyle r^{4}-2a^{2}r^{2}\cos 2\theta =b^{4}-a^{4}}$

参考文献

• Gray, A. "Cassinian Ovals." §4.2 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 82-86, 1997.
• Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, pp. 187-188, 1967.