1.若P0(xo,yo)在椭圆x^2/a^2+y^2/b^2=1外则过 p0做椭圆的两条切线,切点为p1,P2则求证切点弦p1,p2的直线方程是x0x/a^2+y0y/b^2=1;2.若p0(x0,y0)在双曲线x^2/a^2-y^2/b^2=1(a大于0,b大于0)外,则过p0做双曲线的两条
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/26 17:39:21
1.若P0(xo,yo)在椭圆x^2/a^2+y^2/b^2=1外则过 p0做椭圆的两条切线,切点为p1,P2则求证切点弦p1,p2的直线方程是x0x/a^2+y0y/b^2=1;2.若p0(x0,y0)在双曲线x^2/a^2-y^2/b^2=1(a大于0,b大于0)外,则过p0做双曲线的两条
1.若P0(xo,yo)在椭圆x^2/a^2+y^2/b^2=1外则过 p0做椭圆的两条切线,切点为p1,P2则求证切点弦p1,p2的直线方程是x0x/a^2+y0y/b^2=1;
2.若p0(x0,y0)在双曲线x^2/a^2-y^2/b^2=1(a大于0,b大于0)外,则过p0做双曲线的两条切线的切点为p1,p2则求证切点弦p1p2的直线方程是x0x/a^2-y0y/b^2=1
1.若P0(xo,yo)在椭圆x^2/a^2+y^2/b^2=1外则过 p0做椭圆的两条切线,切点为p1,P2则求证切点弦p1,p2的直线方程是x0x/a^2+y0y/b^2=1;2.若p0(x0,y0)在双曲线x^2/a^2-y^2/b^2=1(a大于0,b大于0)外,则过p0做双曲线的两条
首先要知道一个结论:过椭圆上点P(m,n)的切线方程为mx/a^2+ny/b^2=1!
有了上述结论后可以证明如下:
设两个切点为P1(x1,y1),P2(x2,y2),则这两条切线方程为x1x/a^2+y1y/b^2=1,和x2x/a^2+y2y/b^2=1,
由于这两条切线均过P0(x0,y0),所以有x1x0/a^2+y1y0/b^2=1且x2x0/a^2+y2y0/b^2=1,从而说明P1(x1,y1),P2(x2,y2),这两点都过直线x0x/a^2+y0y/b^2=1.而经过两点的直线是唯一的.所以,所求的切点弦直线即为x0x/a^2+y0y/b^2=1
关于双曲线,也同样证之.