椭圆：x²/16+y²/4=1，求过点M（1,1）的弦的中点P的轨迹方程设弦AB，A(x1,y1),B(x2,y2),P(x,y)--->x1+x2=2x, y1+y2=2y∵x1²/16+y²/4=1，x2²/16+y2²/4=1相减：(x1²-x2²)/16+(y1²-y2²)/4=0-- 展开
椭圆：x²/16+y²/4=1，求过点M（1,1）的弦的中点P的轨迹方程设弦AB，A(x1,y1),B(x2,y2),P(x,y)--->x1+x2=2x, y1+y2=2y∵x1²/16+y²/4=1，x2²/16+y2²/4=1相减：(x1²-x2²)/16+(y1²-y2²)/4=0--->2x(x1-x2)/16 = -2y(y1-y2)/4--->AB的斜率K = (y1-y2)/(x1-x2) = (-x)/(4y) = (y-1)/(x-1)--->x(x-1)+4y(y-1)=0--->x²-x+4y²-4y=0--->(x-1/2)²+(2y-1)²=5/4 收起
