|
中点为(x,y)(1)设y=2x+b交椭圆与(X1,Y1),(X2,Y2).X1^2/2+Y1^2=1a式X2^2/2+Y2^2=1b式a-b得:(X1+X2)(X1-X2)/2+(Y1+Y2)(Y1-Y2)=0同时除以(X1-X2),X1+X2=2x,Y1+Y2=2y 得y=1/4x(2)前两步同(1)得:(X1+X2)(X1-X2)/2+(Y1+Y2)(Y1-Y2)=0同时除以(X1-X2),得:(X1+X2)/2+(Y1+Y2)*K=0K=(1-y)/(2-x),代入得x^2+2y^2-2x-2y=0(3)同(2)得:(X1+X2)/2+(Y1+Y2)*K=0P为弦中点,求得K=-1/2直线过P得方程:y=-1/2x+3/4 |
