Question

The set of values of ‘b’ for which the origin and the point (1,1) lie on the same side of the st. line a²x + aby + 1 = 0 ∀ a ∈ R, b > 0 are

(a)   b ∈[2,4)

(b)   b∈(0,2)

(c)  b∈[0,2]

(d) None of these 

Answer 1

Correct option (b)   b∈(0,2)

Explanation:

 (0,0) & (1,1) are on the same side

0 + 1 > 0  so a² + ab + 1 > 0

D < 0 i.e   b² - 4 < 0

b² < 4

-2 < b <  2 but b > 0

b∈(0,2)