The range of values of `alpha` for which the line `2y=gx+alpha` is a normal to the circle `x^2=y^2+2gx+2gy-2=0` for all values of `g` is

Options

A. `[1,oo)`
B. `[-1,oo)`
C. `(0,1)`
D. `(- oo,1]`

Answer

2

Explanation

The line `2y=g x +alpha` should pass through `(-g, -g)` . So, `-2g = -g^(2)+alpha` or `alpha= g^(2)-2g = (g-1)^(2) - ge -1`