1.已知抛物线y^2=2px(p>0)的焦点弦AB的两端点坐标分别为A(x1,y1),B(x2,y2),则y1y2/x1

1个回答

  • 1.(p/2,0)

    y1^2=2px1

    y2^2=2px2

    y1^2y2^2=4p^2x1x2

    y1y2=-2p(x1x2)^1/2

    y1y2/x1x2=-2p/(x1x2)^1/2

    y=k(x-p/2)

    y^2=2px

    k^2(x-p/2)^2=2px

    k^2x^2-pk^2x+1/4p^2k^2-2px=0

    k^2x^2-(pk^2+2p)x+1/4p^2k^2=0

    x1x2=1/4p^2

    y1y2/x1x2=2p/1/2p=4

    A

    2.x^2=4y=2py

    p=2

    y=-1

    x=0

    (x0,y0)

    y0=x0^2/4

    /x0/=/y0+1/

    x0^2=(y0+1)^2=4y0^2

    y0^2+2y0+1=4y0^2

    3y0^2-2y0-1=0

    (3y0+1)(y0-1)=0

    y0=-1/3(she)y0=1

    x0=+-/3,x0=+-2

    (+-2,1)

    r=2

    (x+-2)^2+(y-1)^2=4

    x^2+y^2+-4x-2y+1=0

    B

    3.4-4x+x^2=k^2x^2

    (k^2-1)x^2+4x-4=0

    16+16(k^2-1)=16k^2>0

    2