The line parallel to the x-axis and passing through the intersection of the lines ax+2by+3b=0\; and\; bx-2ay-3a=0,where\; (a,b)\neq (0,0)\; is

  • Option 1)

    below the x- axis at a distance of 2/3 from it

  • Option 2)

    below the x- axis at a distance of 3/2 from it

  • Option 3)

    above  the x- axis at a distance of 2/3 from it

  • Option 4)

    above  the x- axis at a distance of 3/2 from it

 

Answers (1)

As we learnt in 

Line parallel to the y-axis -

x= b

- wherein

The line passes through the point (b,o).

 

 Point of intersection of the lines

\left ax+2by+3b=0 \right ]\times b

\left bx-2ay-3a=0 \right ]\times a

2\left ( b^{2}+a^{2} \right )y=-3\left ( b^{2}+a^{2} \right )

y=\frac{-3}{2}

ax+2b\times \frac{-3}{2}+3b=0

=> x=0

Point of intersection is \left ( 0,\frac{-3}{2} \right )

line parallel to x- axis is below at a distance  \frac{3}{2}\: from\: it.

i.e. y=\frac{-3}{2}


Option 1)

below the x- axis at a distance of 2/3 from it

Incorrect option    

Option 2)

below the x- axis at a distance of 3/2 from it

Correct option

Option 3)

above  the x- axis at a distance of 2/3 from it

Incorrect option    

Option 4)

above  the x- axis at a distance of 3/2 from it

Incorrect option    

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