question_answer

The line parallel to the X-axis and passing through the intersection of the lines \[ax+2\,by+3b=0\]and\[bx-2ay-3a=0,\]where \[(a,b)\ne (0,0)\]is     AIEEE  Solved  Paper-2005

A) above the X-axis at a distance of (2/3) from it

B) above the X-axis at a distance of (3/2) from it

C) below the X-axis at a distance of (2/3) from it

D) below the X-axis at a distance of (3/2) from it

Correct Answer: D

Solution :

Ifandare two lines, then the equation of line passing through the point of intersection ofandwill be. Equation of a line passing through the intersection of linesand is      ...(i) Now, this line is parallel to X-axis, so coefficient of On putting this value in Eq. (i), we get           Therefore, -ve sign shows that the required line is below X-axis at a distancefrom it. Alternate Solution Equations of given lines are                       ...(i) and                             ....(ii) On solving Eqs. (i) and (ii), we get Point of intersection of lines is Also, required line is parallel to X-axis.                             Thus, equation of required line is Hence, the required line is below X-axis at a distancefrom X-axis.