KEAM 2011 Math Paper

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),
abx+2b2y‌‌=−3b2
xab−2a2y‌‌=3a2
−  +   −
────────────
2(a2+b2)y=−3(a2+b2)
⇒‌‌y=−‌

3

2

From Eq. (i), ‌‌c=−‌

3

2

Hence, the line is, y=−‌

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 ‌

3

2