• 2022-07-02
    将下列二次圆锥曲线方程化为标准形,并指出它们的形状:[tex=17.0x1.5]OrndGMXcE2x69J9o+ciHwxzAZZD0/0/7lL+/Y+YC3qkSHpFrpdeMXrCdS+v2yY+K[/tex]
  • 先将二次型[tex=6.0x1.429]fBHdd7aNWTxUysGMHGNVcw9zjv4F1A/BE5opcKHYlrQ=[/tex]用正交变换化为标准形二次矩阵[tex=7.857x2.786]YHIKtHtTy6YeetIBukGWJ/+4CPibC+H1hzFh9VOwgL0WX+Sd1AlwQi+PAQTKavwLntviyHA72xiQci3/QysLvFsnUeCwFr9yl/86T6Mse24=[/tex],解特征方程[tex=7.857x2.786]Uyz5s0rmQIddjb5Jc2T/Yd3zOa6coX2DKX6hnFTniiXajocD3RENFUM7CJIPcHmIwHe7DjL8wQld9a3LFGh7X+VFV1jz3jN6keI9HqGCm7k=[/tex],得其特征值为[tex=4.929x1.214]vxDz5HFQoWDWFqg+n81e8kcJJWxUZh+ShzgOVcGj8UQ=[/tex]相应地,特征向量为[tex=11.5x2.786]qulE2au0sCsC2RUF6/a3J3NtG8/hCqny8tlhGzhMKwPAOdb4n41GaR7t6YxrKMs4NtjeqZfBrFXaw3OMzk3LNZ+Ino2+xthvFXoQKrAqImrDWQJqjIeF/25ymToH5b1666prEMetdlEFJmI5W48XnvRwjgxk/3SFXP7flSVAtFvjhtIhqrUjDP4g1iknR1n59PjKUi2sOjp9KMy+zIsJcQ==[/tex],正交单位化得[tex=14.786x2.786]4IwCB7mUZT1bCJOXMr2ql/WD4Jr7xQa6wNu3u7bSc77DLrLeOScuy/YTuN1xT5WGfy9k3CB6diIGoXvApMBT2OPYw//3r35gNx/n4hws2GgzaDhSkOU/YBDZCEMzD27+Omq05RVyitzGj2MDGAB17DU0iytVEsYiAdUzBDOvSwIN2qDsza9YByhnMG2inY5gCqM72Lb/hrpsJx5b5v8f14UE6fxrUPns5oPA5V5Bg2s=[/tex].作正交变换[tex=14.214x2.786]075gCzZzsMRb6HYXYk9X91xtdU1wg4Ye92uOi7+SMR/bto4PrzAtGjJBH8AvvMII7SqJytvW20sIBrN0eNMVSzpACk43W0uT5P+6FiHqFfTxL4V+kB0YQszmNw55nZ2YJqVAn5an3ZmyYwNlwG/N/sBmYn2GRizUzheqCQGgXU+W/wgmbbaFFJPKUEIzMNMyiIt9GBODXvAvNACZcWsiwvusKKVbAPMg69OCHeG6SOob1HO1quaSFprDncH6elBw[/tex],将原二次圆锥曲线化为[tex=13.286x2.929]3BOtYbEICLRScenFum2MYsllSszT6CbDPGEH98iD3Q8dLhOF3gM+0DUQwVJPnfwLlHiMhG1Qf0pOHs5M97WT4A==[/tex]则标准形为[tex=13.071x2.929]ZOPZJzMoZFKInF6NBoUipaCx2v1cHtCFuO3KpAqHfvGHfEbRJF5CoodUyb31JGQQZeZYIifzOF+UONUlzGhgQIUTaV2I+IjpOY4Q14E8NT2dM/BXDVagN6Qvmk1YogQn[/tex],所以它表示的是抛物线。
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    内容

    • 0

      下列方程中,为二元一次方程的是() A: 3 x = 2 y B: 3 x ﹣ 6 = 0 C: 2 x ﹣ 3 y = xy D: x ﹣ = 0

    • 1

      【单选题】分段函数: ,下面程序段中正确的是__________。 A. If x < 0 Then y = 0 If x < 1 Then y = 1 If x < 2 Then y = 2 If x >= 2 Then y = 3 B. If x >= 2 Then y = 3 If x >= 1 Then y = 2 If x > 0 Then y = 1 If x < 0 Then y = 0 C. If x < 0 Then y = 0 ElseIf x > 0 Then y = 1 ElseIf x > 1 Then y = 2 Else y = 3 End If D. If x > =2 Then y = 3 ElseIf x > =1 Then y = 2 ElseIf x > =0 Then y = 1 Else y = 0 End If

    • 2

      下面程序段中正确的是( )。 A: If x<0 Then y=0 If x<1 Then y=1 If x<2 Then y=2 If x>=2 Then y=3 B: If x>=2 Then y=3 If x>1 Then y=2 If x>=0Then y=1 If x>0 Then y=0 C: If x<0 Then y=0 Else If>=0Then y=1 Else y=3 End If D: If x>=2 Then y=3 Else If>=1 Then y=2 Else y=0 End If

    • 3

      反应X+2Y→Z是一个2.5级反应,下面的速率方程式中,可能正确的是()(A)v=kc(X)&#91;c(Y)&#93;2;(B)v=kc(X)&#91;c(Y)&#93;3/2;(C)v=k&#91;c(X)&#93;2c(Y);(D)v=k&#91;c(X)&#93;0&#91;c(Y)&#93;2 A: v = k c (X)[c (Y)]2; B: v = k c (X)[ c (Y)]3/2; C: v = k[c (X)]2 c (Y); D: v = k [c (X)]0[ c (Y)]2

    • 4

      3、反应X+2Y→Z是一个2.5级反应,下面的速率方程式中,可能正确的是..(A)v=kc(X)&#91;c(Y)&#93;2;(B)v=kc(X)&#91;c(Y)&#93;3/2;(C)v=k&#91;c(X)&#93;2c(Y);(D)v=k&#91;c(X)&#93;0&#91;c(Y)&#93;2 A: (A) v = k c (X)[c (Y)]2; B: (B) v = k c (X)[ c (Y)]3/2; C: (C) v = k[c (X)]2 c (Y); D: (D) v = k [c (X)]0[ c (Y)]2