A) above the x-axis at a distance of\[\frac{3}{2}\]
B) above the x-axis at a distance of\[\frac{2}{3}\]
C) below the x-axis at a distance of\[\frac{2}{3}\]
D) below the x-axis at a distance of\[\frac{3}{2}\]
E) below the x-axis at a distance of 3
Correct Answer: D
Solution :
Let the line parallel to\[x-\]axis is, \[y=c\] ...(i) Given lines, \[ax+2by=-3b\] ...(ii) \[bx-2ay=3a\] ...(iii) Multiply by b in Eq. (ii) and by a in Eq. (iii), then subtract Eq. (ii) from Eq. (iii), \[\begin{align} & \underline{\begin{align} & abx+2{{b}^{2}}y=-3{{b}^{2}} \\ & xab-2{{a}^{2}}y=3{{a}^{2}} \\ & -\,\,\,\,\,\,\,\,+\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,- \\ \end{align}} \\ & 2({{a}^{2}}+{{b}^{2}})y=-3({{a}^{2}}+{{b}^{2}}) \\ \end{align}\] \[\Rightarrow \] \[y=-\frac{3}{2}\] From Eq. (i), \[c=-\frac{3}{2}\] Hence, the line is, \[y=-\frac{3}{2}\] Which is passing through the point of intersection of the lines Eqs. (ii) and (iii) below the\[x-\]axis at a distance of\[\frac{3}{2}\].
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