P (a, b) is the midpoint of a line segment between axes. Show that equation of the line is `x/a+y/b=2.`

Explanation

Let equation of the line is
`(x)/(p)+(y)/(q)=1`………`(1)`
This line intersects `x`-axis at point `A(p,0)` and `y`-axis at point `B(0,q)`.
The mid-point of line segment `AB` is `(a,b)`.
`:. (p+0)/(2)=aimpliesp=2a`
and `(0+q)/(2)impliesq=2b`
From equation `(1)`,
`(x)/(2a)+(y)/(2b)=1implies (x)/(a)+(y)/(b)=2`