如图,P是双曲线x^2/a^2-y^2/b^2=1上异于顶点的任意一点,实轴端点为A,B,PA,PB 分别交y轴于M,N,求证;求证;OM的绝对值乘ON的绝对值为定值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 12:56:40
![如图,P是双曲线x^2/a^2-y^2/b^2=1上异于顶点的任意一点,实轴端点为A,B,PA,PB 分别交y轴于M,N,求证;求证;OM的绝对值乘ON的绝对值为定值](/uploads/image/z/6954837-69-7.jpg?t=%E5%A6%82%E5%9B%BE%2CP%E6%98%AF%E5%8F%8C%E6%9B%B2%E7%BA%BFx%5E2%2Fa%5E2-y%5E2%2Fb%5E2%3D1%E4%B8%8A%E5%BC%82%E4%BA%8E%E9%A1%B6%E7%82%B9%E7%9A%84%E4%BB%BB%E6%84%8F%E4%B8%80%E7%82%B9%2C%E5%AE%9E%E8%BD%B4%E7%AB%AF%E7%82%B9%E4%B8%BAA%2CB%2CPA%2CPB+%E5%88%86%E5%88%AB%E4%BA%A4y%E8%BD%B4%E4%BA%8EM%2CN%2C%E6%B1%82%E8%AF%81%EF%BC%9B%E6%B1%82%E8%AF%81%EF%BC%9BOM%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%B9%98ON%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%B8%BA%E5%AE%9A%E5%80%BC)
如图,P是双曲线x^2/a^2-y^2/b^2=1上异于顶点的任意一点,实轴端点为A,B,PA,PB 分别交y轴于M,N,求证;求证;OM的绝对值乘ON的绝对值为定值
如图,P是双曲线x^2/a^2-y^2/b^2=1上异于顶点的任意一点,实轴端点为A,B,PA,PB 分别交y轴于M,N,求证;
求证;OM的绝对值乘ON的绝对值为定值
如图,P是双曲线x^2/a^2-y^2/b^2=1上异于顶点的任意一点,实轴端点为A,B,PA,PB 分别交y轴于M,N,求证;求证;OM的绝对值乘ON的绝对值为定值
不防设A(-a,0),B(a,0),P(xo,yo).则直线PA、PB方程分别为y1=[yo/(xo+a)](x+a),y2=[yo/(xo-a)](x-a),分别令x=0得yM=ayo/(xo+a),yN-ayo/(xo-a),那么lOMllONl=lyMyNl=(ayo)^2/(xo^2-a^2),又P(xo,yo)在双曲线上则有yo^2=(b^2)(xo^2-a^2)/a^2,代入上式,得lOMllONl=b^2(定值)证毕!注:符号"^"表示平方.
不防设A(-a,0),B(a,0),P(xo,yo).则直线PA、PB方程分别为y1=[yo/(xo+a)](x+a),y2=[yo/(xo-a)](x-a),分别令x=0得yM=ayo/(xo+a),yN-ayo/(xo-a),那么lOMllONl=lyMyNl=(ayo)^2/(xo^2-a^2),又P(xo,yo)在双曲线上则有yo^2=(b^2)(xo^2-a^2)/a^2,代入上式,得lOMllONl=b^2(定值)证毕!注:符号"^"表示平方。