In ur question,

y=2tan^-1((x-a)/(b-x))

Differentiating both sides wrt x,

dy/dx = 2/((x-a)/(b-x) +1)  [ ((((b-x))/2 (x-a)) - (((x-a))(-1)/2(b-x)) ] / (b-x)

On solving ,

dy/dx = 1/(b-x)(x-a)

Squaring both sides,

(dy/dx)² = 1/(b-x)(x-a)

(dy/dx)²+1/(x-a)(x-b) = 0

Kindly compute ur question -"such" to "show"