The range of `'alpha'` for which the point `(alpha, alpha)` lies in minor arc bounded by the curves `x^(2)+y^(2)=1` and `x+y=1` is

Options

A. `(1)/(2)lt alpha (1)/(sqrt(2))`
B. `-(1)/(sqrt(2)) lt alpha lt (1)/(sqrt(2))`
C. `alpha gt (1)/(2)`
D. `0 lt alpha lt (1)/(2)`

Answer

A

Explanation

The range of ………
Point `(alpha, alpha)` will lie is shaded regin
it `alpha^(2)+alpha^(2)-1lt0`
`implies 2a^(2)-1lt0`
`implies - (1)/(2)lt alpha lt (1)/(sqrt(2))` ….(1)
and `alpha+alpha-1 implies gt (1)/(2)` ….(2)
`:.` common solution of (1) and (2) is :
`(1)/(2)lt alpha lt (1)/(sqrt(2))`