Hi

I need help with this question:

a curve

square root(x) + Square root (y) = 1(eqn 1), for x and y bigger and equal too zero

Show that the sum of x any y intercepts of the tangent line to any point (a,b) on the curve (a,b bigger than 0) is equal to one

This is what i have done so far

Used implicit differentiation to find dy/dx of the eqn 1

It gives

dy/dx=-sqrt(y)/sqrt(x)

from there used y=mx+c

So m=-sqrt(y)/sqrt(x)

an then i subbed (a,b) into dy/dx to find m

so

that is y=(-sqrt(b)/sqrt(a))x+ c

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