椭圆和双曲线焦点弦公式是什么

1个回答

  • 椭圆:

    (1)焦点弦:A(x1,y1),B(x2,y2),AB为椭圆的焦点弦,M(x,y)为AB中点,则L=2a±2ex

    (2)设直线;与椭圆交于P1(x1,y1),P2(x2,y2),且P1P2斜率为K,则

    |P1P2|=|x1-x2|√(1+K²)或|P1P2|=|y1-y2|√(1+1/K²)

    双曲线:

    (1)焦点弦:A(x1,y1),B(x2,y2),AB为双曲线的焦点弦,M(x,y)为AB中点,则L=-2a±2ex

    (2)设直线;与双曲线交于P1(x1,y1),P2(x2,y2),且P1P2斜率为K,则

    |P1P2|=|x1-x2|√(1+K²)或|P1P2|=|y1-y2|√(1+1/K²){K=(y2-y2)/(x2-x1)}

    抛物线:

    (1)焦点弦:已知抛物线y²=2px,A(x1,y1),B(x2,y2),AB为抛物线的焦点弦,则

    |AB|=x1+x2+p或|AB|=2p/(sin²H){H为弦AB的倾斜角}

    (2)设直线;与抛物线交于P1(x1,y1),P2(x2,y2),且P1P2斜率为K,则

    |P1P2|=|x1-x2|√(1+K²)或|P1P2|=|y1-y2|√(1+1/K²){K=(y2-y2)/(x2-x1)}