The set of values of b for which the origin a | vedclass

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(B) Let the line be $L(x, y) = a^2x + aby + 1 = 0$.For the origin $(0, 0)$,$L(0, 0) = 0 + 0 + 1 = 1$,which is positive.For the points to lie on the sa

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$b \in (0, 2)$

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(B) Let the line be $L(x, y) = a^2x + aby + 1 = 0$.For the origin $(0, 0)$,$L(0, 0) = 0 + 0 + 1 = 1$,which is positive.For the points to lie on the same side,$L(1, 1)$ must also be positive for all $a \in R$.$L(1, 1) = a^2(1) + ab(1) + 1 = a^2 + ab + 1 > 0$.This is a quadratic expression in $a$ with a positive leading coefficient $(1 > 0)$.For this to be positive for all $a \in R$,the discriminant $D$ must be less than $0$.$D = (b)^2 - 4(1)(1) $b^2 - 4 $(b - 2)(b + 2) This implies $-2 Given that $b > 0$,the intersection of these conditions is $b \in (0, 2)$.

The set of values of $b$ for which the origin and the point $(1, 1)$ lie on the same side of the straight line $a^2x + aby + 1 = 0$ for all $a \in R$ and $b > 0$ is:

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