超難的數學Word Problem!!!!!!!! 請高手入

Let the equation is x/a + y/b = 1...(1) where a,b > 0

Then the area is ab/2 (as it should be a right-angle triangle)

Sub.(3,5) into (1) we can find out the relationship between a and b

3/a + 5/b = 1

5a + 3b = ab

b = 5a/(a - 3)

Sub. into ab/2 => (5/2) a^2/(a - 3)

Let y = a^2/(a - 3)

ln y = 2lna - ln(a - 3)

differentiate w.r.t a, 2/a - 1/(a - 3)

Let 2/a - 1/(a - 3)= 0

2a - 6 = a

a = 6 => b = 10

The equation is x/6 + y/10 = 1

To : 翻雷滾天 風卷殘雲
"the line through the point (3,5)", it seems you are calc it pass thru' (5,3).

m2 = 9/50 ----------------------------------------- m2 = 9/25 ???

m = - 3/(5√2) since m is negative ----------------------------------------- m = 3/5 ???
_______________________________

d2A/dm2 > 0 (so A is min.)

Hence equation is:

- 3x/(5√2) - y + (3 + 3/√2) = 0

3x + (5√2)y - (15√2 + 15) = 0