设直线:y=kx①,A(x1,y1)B(x2,y2),M(x,y)
圆O:(x-3)²+(y-2)²=4②
①②:(k²+1)x²-(6+4k)x+9=0
x1+x2=2x=(6+4k)/(k²+1)③,y1+y2=2y=k(6+4k)/(k²+1)④
OM⊥AB:(y2-y1)/(x2-x1)*(y-2)/(x-3)=-1即:-1/k=(y-2)/(x-3)⑤
③④或者④⑤均可解出
设直线:y=kx①,A(x1,y1)B(x2,y2),M(x,y)
圆O:(x-3)²+(y-2)²=4②
①②:(k²+1)x²-(6+4k)x+9=0
x1+x2=2x=(6+4k)/(k²+1)③,y1+y2=2y=k(6+4k)/(k²+1)④
OM⊥AB:(y2-y1)/(x2-x1)*(y-2)/(x-3)=-1即:-1/k=(y-2)/(x-3)⑤
③④或者④⑤均可解出