圆x^2+y^2=8内有一点p(-1,2),AB为过点p且倾斜角为a的弦

1个回答

  • 1.ab绝对值3.5:

    y-2=tan135°(x+1)与x^2+y^2=8组合求解;既x+y=1与(x+y)^2-2xy=8组合求解可得.

    2.y=1/2(x+5):

    假设坐标A(x1,y1),B(x2,y2),由于在p点平分,

    所以x1-(-1)=-1-x2既x1+x2=-2;y1-2=2-y2既y1+y2=4.

    将x1^2+y1^2=8与x2^2+y2^2=8组合相减得x1^2-x2^2+y1^2-y2^2=0再简化得(y1-y2)(y1+y2)=-(x1-x2)(x1+x2);将x1+x2=-2和y1+y2=4代入得

    (y1-y2)/(x1-x2)=1/2既斜率等于1/2,

    知道一点和斜率便 可求得直线方程得y-2=1/2(x+1),简化便得.

    3.y^2+x^2-2y+x=0:

    A(x1,y1),B(x2,y2),m(x,y)得由于AB在m点平分,

    所以x1-x=x-x2既x1+x2=2x;y1-y=y-y2既y1+y2=2y;

    将x1^2+y1^2=8与x2^2+y2^2=8组合相减得x1^2-x2^2+y1^2-y2^2=0再简化得(y1-y2)(y1+y2)=-(x1-x2)(x1+x2);将x1+x2=2x和y1+y2=2y代入得(y1-y2)/(x1-x2)=-x/y既斜率为-x/y.

    又因为斜率等于p点与没点斜率(y-2)/(x+1),

    所以-x/y=(y-2)/(x+1),得y^2+x^2-2y+x=0