Question

如图直线L交于x轴y轴分别于AB两点,A(a,0),B(0,b),且(a- b)2+|b-4|=0 求A,B两点坐

Answer 1

1.由(a- b)^2+|b-4|=0 ,得a=b=4,

∴A(4,0),b(0,4).

2.C(3,1).设P(0,p),p>0,

CP的斜率k1=(1-p)/3,CO的斜率k2=1/3,

tanOCP=(k2-k1)/(1+k2k1)=(p/3)/[1+1/3*(1-p)/3]=3p/(10-p)=1,

3p=10-p,p=2.5.

∴P(0,2.5).

3.作CH⊥OA于H,则H(3,0)在A,E之间,

易知△BOD∽△CHE∽△OHC,

∴OD/OB=HE/HC=HC/HO=1/3,

∴OD=4/3,HE=1/3,

∴AE=AH+HE=4/3=OD.