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If the lines a1x+b1y+1=0,\ a2x+b2y+1=0\ ...

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.

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To show that the points \((a_1, b_1)\), \((a_2, b_2)\), and \((a_3, b_3)\) are collinear given that the lines \(a_1x + b_1y + 1 = 0\), \(a_2x + b_2y + 1 = 0\), and \(a_3x + b_3y + 1 = 0\) are concurrent, we can follow these steps: ### Step 1: Understand the concept of concurrency Three lines are said to be concurrent if they intersect at a single point. This means that there exists a point \((x_0, y_0)\) such that all three line equations are satisfied simultaneously. ### Step 2: Set up the equations The equations of the lines can be rewritten as: 1. \(a_1x + b_1y + 1 = 0\) (Equation 1) ...
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