Let all chords of parabola `y^(2)=x+1` which subtends right angle at `(1,sqrt(2))` passes through `(a,b)` then the value of `a+b^(2)` is

Answer

4

Explanation

Shifting origin at `(1,sqrt(2))`
`(Y+2sqrt(2))^(2)=X+1+1,y=Y+sqrt(2),x=X+1`
`Y^(2)+(2sqrt(2)Y-X)((Y-mX)/C)=0`
`1+(2sqrt(2))/C+m/C=0`
`C+m+2sqrt(2)=0`
`Y=mx-=m-2sqrt(2)`
`y-sqrt(2)=m(x-1)-m-2sqrt(2)`
it is passes through `(a,b)AAm`
`impliesa=2` and `b=-sqrt(2)`