Question

If a+b=8 then what is the equation of the locus of a moving point which is always mid-point of (a,0) and (0,b) ?

Answer 1

Desired locus is `y=4-x`

Explanation:

Let the movving point be `(x,y)`.

As it is the midpoint of `(a,0)` and `(0,b)`

or `(a,0)` and `(0,8-a)`, we have

`x=a/2` and `y=(8-a)/2=4-a/2`

Eliminating `a` we have

`y=4-x`, which is the desired locus.