longshang123
花朵
共回答了13个问题采纳率:100% 举报
(1) OA = OB,A(a,0),B(0,a),a > 0
直线l的方程:x/a + y/a = 1,x + y = a
过点P(2,1):2 + 1 = a
x + y = 3
(2)
A(a,0),a > 0
B(0,b),b > 0
2 = (a + 0)/2,a = 4
1 = (0 + b)/2,b = 2
直线l的方程:x/4 + y/2 = 1
(3)
令斜率为k (k < 0),直线l的方程:y - 1 = k(x - 2),
x = 0,y = 1 - 2k,B(0,1 - 2k)
y = 0,x = 2 - 1/k,A(2 - 1/k,0)
S = (1/2)(2 - 1/k)(1 - 2k) = (1/2)(4 - 4k - 1/k) = 6
4k² + 8k + 1 = 0
k = -1 ± √3/2
y = (-1 + √3/2)x + 3 -√3)
或
y = (-1 - √3/2)x + 3 +√3)
(4)
OA + OB = 1 - 2k + 2 - 1/k = 3 -2k - 1/k ≥ 3 + 2√[-2k)(-1/k)] = 3 + 2√2
-2k = -1/k时等号成立,k² = 2
k = -√2 (舍去k = √2 > 0)
1年前
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