Question

如图,M为双曲线y=根号3/x一点,过点M作x轴,y轴的垂线,分别交直线y=负x+m于D,C两点

Answer 1

设M坐标为（x0,y0),

根据双曲线函数,y=√3/x,

A（0,m),

B(m,0),

y0=√3/x,

∴M（x0,√3/x0)

D(x1,y1),

y1=-x1+m,

x1=x0,

y1=-x0+m,

∴D(x0,-x0+m),

C(x2,y2),

y2=-x2+m

y2=y0=√3/x0,

x2=m-y2=m-√3/x0,

∴C(m-√3/x0,√3/x0),

AD=√[(x0-0)^2+(-x0+m-m)^2]=√2m,

BC=√[（m-m+√3/x0)^2+(0-√3/x0)^2]

=√（3/x0^2+3/x0^2)

=√6/x0,

∴|AD|*|BC|= √2m*√6/m

=2√3.