已知点A(3,4),B(-2.m)在反比例函数Y=K/X的图像上,经过点A、B的一次函数的图像分别与x轴、y轴交于点C、

1. y = k/x, 4 = k/3, k = 12
y = 12/x
2. -2 = 12/m, m = -6
B(-2, -6)
A(3, 4)
过点A、B的一次函数的解析式: (y +6)/(x + 2) = (4+6)/(3+2) = 2
y = 2x -2
2x - y -2 =0
3. |AB| = √[(2+3)² + (4+6)² = 5√5
AB上的高为O与AB的距离=|2*0 - 0 -2|/√(4+1) = 2/√5
△ABO的面积为(1/2)(5√5)(2/√5)=5
4．见图,x < -2或 0 < x < 3
5. y = 2x -2, y = 0, x = 1, C(1, 0)
P(0, p)
d = PA + PC = √[9+(p-4)²] + √(1+p²)
d' = (p-4)/√[9+(p-4)²] + p/√(1+p²) = 0
(p-4)²/[9+(p-4)²] = p²/(1+p²)
(p-4)²/9 = p²
p² + p -2 = 0
(p+2)(p-1) = 0
p = -2或 p =1
P(0, -2)或P(0, 1)
6. H(0, h)
(i) OH = OA
OH² = OA²
h² = 3² + 4² = 25
h = ±5
H(0, 5)或H(0, -5)
(ii) AH = OA
3² + (h-4)² = 3² + 4²
h-4 = ±4
h = 8或h=0 (原点,舍去)
H(0, 8)
(iii)AH = OH
3² + (h-4)² = h²
h = 25/8
H(0, 25/8)