圆锥曲线性质一览表

圆锥曲线性质一览表性质椭圆双曲线抛物线定义｛P||PF1|+|PF2|=2a｝｛P|||PF1|-|PF2||=2a｝｛P|dPF||=e(e=1)｝｛P|dPF||=e(0e1)｝｛P|dPF||=e(e1)｝简图标准方程)0(12222babyax)0(12222babxay)0,0(12222babyax)0,0(12222babxayy2=2pxy2=-2pxx2=2pyx2=-2py范围|x|≤a|y|≤b|y|≤a|x|≤b|x|≥ay∈R|y|≥ax∈Rx≥0y∈Rx≤0y∈Ry≥0x∈Ry≤0x∈R对称性轴对称：x轴、y轴中心对称：原点（0,0）轴对称：x轴、y轴中心对称：原点（0,0）轴对称：x轴、y轴中心对称：原点（0,0）轴对称：x轴、y轴中心对称：原点（0,0）轴对称：x轴轴对称：y轴焦点F1(-c,0)F2(c,0)F1(0,-c)F2(0,c)F1(-c,0)F2(c,0)F1(0,-c)F2(0,c)F)0,2(pF)0,2(pF)2,0(pF)2,0(p顶点A1(-a,0)A2(a,0)B1(0,-b)B2(0,b)A1(0,-a)A2(0,a)B1(-b,0)B2(b,0)A1(-a,0)A2(a,0)A1(0,-a)A2(0,a)(0,0)(0,0)(0,0)(0,0)焦半径a±ex0(左加右减)a±ey0(下加上减)|ex0±a|(左加右减)|ey0±a|(下加上减)02xp02xp02yp02yp准线cax2cay2cax2cay22px2px2py2py焦参数cb2cb2cb2cb2pppp离心率ace(0e1)ace(0e1)ace(e1)ace(e1)e=1e=1e=1e=1三角形2tan2b2tan2b渐近线xabyxbay通径ab22ab22ab22ab222p2p2p2p结论22*abKKOMAB22*baKKOMAB22*abKKOMAB22*baKKOMAB0*xpKKOMAB0*xpKKOMAB0*ypKKOMAB0*ypKKOMAB切线12020byyaxx12020bxxayy12020byyaxx12020bxxayy)(00xxpyy)(00xxpyy)(00yypxx)(00yypxx弦长212212212212*4)(*114)(*k1|AB|yyyykxxxx