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) ?

1 Answer
Sep 11, 2017

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.