P(0,1),设中点为M(x,y)
圆的标准方程为:(x+1)²+y²=1
圆心C(-1,0)
画图可知:CM⊥PM
向量CM=(x+1,y),向量PM=(x,y-1)
x(x+1)+y(y-1)=0
x²+y²+x-y=0
所以,中点M的轨迹方程为:x²+y²+x-y=0,且(x+1)²+y²
x^2+y^2+2x=0x^2+2x+y^2=0x^2+2x+1+y^2=1(x+1)²+y²=1
向量cm和pm,是代入哪一题式得出x(x+1)+y(y-1)=0
CM⊥PM所以,向量CM*向量PM=0向量CM=(x+1,y),向量PM=(x,y-1)向量CM*向量PM=x(x+1)+y(y-1)所以:x(x+1)+y(y-1)=0