If the line `|y| = x -alpha`, such that `alpha > 0` does not meet the circle `x^2 + y^2 - 10x + 21 = 0`, then `alpha` belongs to

Options

A. `(0,5-2sqrt(2))uu (5+2sqrt(2),oo)`
B. `(5-2sqrt(2),5+2sqrt(2))`
C. `(5-2sqrt(2),7)`
D. none of these

Answer

C

Explanation

`x = |y| - alpha = 0`
Centre `-= (5,0),` Radius =2
Perpendicular distance from centre to the line `gt` Radius
`rArr|(5-|0|-alpha)/(sqrt(1+1))|gt2`
`rArr |5-alpha| gt 2 sqrt(2)`
`rArr 5-alpha gt 2 sqrt(2)` or `5-alpha lt -2 sqrt(2)`
`rArr alpha lt 5 -2 sqrt(2)` or `alpha gt5 +2 sqrt(2)`