A simpler form is giving . That immediately gives as you have.

Very good!then i subbed a(a,b) into y=(-sqrt(b)/sqrt(a))x+ c to find c

i found c= b+sqrt(ab)

from there i tried to find the x-intercept(used y=0) an y-intercept(used x=0)

so i found that x-int=sqrt(ab)-a

and y-int=b+sqrt(ab)

from there i've tried to relate it to original equation somehow but cannot relate it so that the sum of the intercepts equals 1

Any help would be appreciated, thank you

With x= 0, and with y= 0, so , . That is not exactly what you got- notice the "+ a" in the y-intercept.

and you ought to be able to recognize that as a "perfect square": !

Now, use the fact that (a, b) is on the given curve so .