InterviewSolution
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InterviewSolution
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Find the value of `lambda`, if the line `3x-4y-13=0,8x-11 y-33=0a n d2x-3y+lambda=0`are concurrent. |
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Answer» The given lines are concurrent if `|{:(3,-4,13),(8,-11,-33),(2,-3,lambda):}| = 0` `" or " 3(-11lambda-99) +4(8lambda+66)-13(-24+22)=0` ` " or " -lambda-7=0` `" or " lambda=-7` Alternative method: The given equations are `3x-4y-13=0 " " (1)` `8x-11y-33=0 " " (2)` `" and " 2x-3y+lambda=0 " " (3)` Solving (1) and (2), we get x =11 and y=5 Thus, (11,5) is the point of intersection of (1) and (2). The given lines will be concurrent if they pass through a common point, i.e., the point of intersection of any two lines lies on the third. Therefore, (11,5) lies on (3), i.e., `2 xx 11-3 xx 5+lambda=0` `" or " lambda=-7` |
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