If the set of `'K'` for which two distinct chords of the ellipse `(x^(2))/8+(y^(2))/2=1` passing through `(2,-1)` are bisected by the line `x+y=K` is `[a,b]` then `(a+b)` is…………

Answer

1

Explanation

Equation of cord whose mid-point is `(t,K-t)`
`(tx)/8+((K-t)y)/2=(t^(2))/8+((K-t)^(2))/2`…………..(i)
`(2,-1)` satisfy (i)
`implies5t^(2)-(6+8K)t+4(K^(2)+K)=0`
For two distinct chords,
`Dgt0`
`(6+8K)^(2)-4.4.5(K^(2)+K)gt0`
`implies4K^(2)-4K-9lt0`
`Kepsilon[(1-sqrt(10))/2,(1+sqrt(10))/2]impliesa+b=1`