If the lines`a_1x+b_1y+1=0,\ a_2x+b_2y+1=0\ a n d\ a_3x+b_3y+1=0`
are concurrent, show that the points `(a_1, b_1),\ (a_2, b_2)a n d\ (a_3, b_3)`
are collinear.
Text Solution
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The given lines are `a_(1)x+b_(1)y+1=0 " "(1)` `a_(2)x+b_(2)y+1=0 " "(2)` `"and " a_(3)x+b_(3)y+1=0 " "(3)` If these lines are concurrent, we must have `|{:(a_(1),b_(1),1),(a_(2), b_(2), 1),(a_(3),b_(3),1):}| =0` which is the condition of the collinearity of these points `(a_(1), b_(1)),(a_(2), b_(2)) " and " (a_(3), b_(3)).` Hene, if the given lines are concurrent, the given points are collinear.
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