Question

The set of values of 'b' for which the origin and the point $(1,1)$ lie on the same side of the straight line, $a^{2}x+aby+1=0\forall a\in R,b>0$ are?

• A. $b\in (2,4)$
• B. $b\in (0,2)$
• C. $b\in [0,2]$
• D. $(2,\infty )$

Answer 1

The correct option is B $b\in (0,2)$

$\begin{array}{c}{a}^{2}x+aby+1=0b>0\\ putx=0\&y=0,weget\\ a^2\left(0\right)+ab\left(0\right)+1>0\\ a^2\left(1\right)+ab\left(1\right)+1>0\\ a^2\left(1\right)+ab\left(1\right)+1>0\\ a^2+ab+1>0\forall a\in R\\ b^2-4<0\\ b\in \left(-2,2\right)\\ b>0\left(given\right)\\ \therefore b\in \left(0,2\right)\\ Hence,theoptionBisthecorrrectanswer.\end{array}$