if P(x,y) is any point on the line joining the points A(a,0) and B(0,b) then show that x/a+y/b=1

Asked by  | 5th Jan, 2010, 08:16: PM

Expert Answer:

Using the slope form of the line,

 (y - 0)/(x - a) = (b - y)/(0 - x) ..........(Slope between P and A must be equal to the slope between B and P)

y/(x - a) = (b - y)/-x

(b - y)(x - a)/(-xy) = 1

(bx - ab - xy + ay)/(-xy) = 1

1 + ab/(xy) - b/y - a/x = 1

ab/(xy)  =  b/y + a/x

ab/(xy) = (bx + ay)/(xy)

x/a + y/b = 1

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Answered by  | 5th Jan, 2010, 08:45: PM

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