If the line `y = mx` does not intersect the circle `(x+10)^2 + (y +10)^2=180,` then

Options

A. `m in (-2, oo)`
B. `m in (-oo, -1//2)`
C. `m in (-2, -1//2)`
D. none of these

Answer

C

Explanation

The line y=mx will not intersect the circle `(x+10)^(2)+(y+10)^(2)=180`, if
Length of perpendicular from the centre `gt` radius
`rArr |(-10m +10)/(sqrt(m^(2)+1))|gt sqrt(180)`
`rArr 100(m-1)^(2) gt 180 (m^(2)+1)`
`rArr 2m^(2) + 5m + 2 lt 0`
`rArr (2m +1)(m+2)lt0rArr-2 lt m lt - (1)/(2) rArr m in (-2, -1//2)`