Question

The value of \(p\), for which the pair of equations \(3x + 4y + 2 = 0\) and \(9x + py + 8 = 0\) represents parallel lines, is:

• A. 2
• B. 4
• C. 6
• D. 12

Hint:

When two lines are parallel, their slopes must be equal. Use the slope formula \(-\frac{A}{B}\) for lines in the form \(Ax + By + C = 0\).

Answer 1

The Correct Option is B

For the two lines to be parallel, their slopes must be equal. The slope of the equation \(Ax + By + C = 0\) is given by \(-\frac{A}{B}\). For the first equation \(3x + 4y + 2 = 0\), the slope is \(-\frac{3}{4}\). For the second equation \(9x + py + 8 = 0\), the slope is \(-\frac{9}{p}\). For the lines to be parallel, we set the slopes equal to each other: \[ -\frac{3}{4} = -\frac{9}{p} \] Solving for \(p\), we get: \[ p = 4 \] Thus, the correct answer is option (2).