Question

# Find the value of $$k$$ for which the lines $$x+2y+3=0$$ and  $$8x+ky-1=0$$ are parallel.

Solution

## We havex+2yy+3=02x−by+5=0and, 8x+ky-1=ax+3y=2Now,x+2y+3=02x−by+5=0or, 2y=-x-3by=2x+5or $$y = \frac{{ - x}}{2} - \frac{3}{2}$$Slope of the line  $$= -\frac{2}{b}$$Again$$8x+ky-1=0$$or $$ky=-8x+1$$or $$y = \frac{{ - 8}}{R} + \frac{1}{R}$$Solpe of the is line $$= \frac{{ - 8}}{R}$$$$\because$$ The lines are parallel, so the slopes of the two lines are equal $$\therefore \frac{{ - 1}}{2} = \frac{{ - 8}}{R}\,\,or\,\,R = 16$$Hence, which is the required answer.Mathematics

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