If points `(a ,0),\ (0, b)a n d\ (x , y)` are collinear, using the concept of slope prove that `x/a+y/b=1.`

Explanation

The correct option is` A`
`frac{x}{a}+frac{y}{b}=1`

Let` A(a, O), B(O, b)` and` P(x, y) `be the collinear points.

`Rightarrow Slope of A B= Slope of BP`

`Rightarrow frac{b-0}{0-(-a)}=frac{y-b}{x-0} `

`Rightarrow frac{-b}{a}=frac{y-b}{x} `

`Rightarrow-x b=a y-a b `

`Rightarrow x b+a y=a b `

`Rightarrow frac{x}{a}+frac{y}{b}=1`