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Let a x+b y+c=0 be a variable straight l...

Let `a x+b y+c=0` be a variable straight line, whre `a , ba n dc` are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

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To solve the problem, we need to prove that the variable straight line \( ax + by + c = 0 \) passes through a fixed point, where \( a, b, c \) are the first, third, and seventh terms of an increasing arithmetic progression (AP), respectively. ### Step-by-Step Solution: 1. **Define the terms of the AP**: Let the first term of the AP be \( a \). The common difference of the AP is denoted as \( d \). Thus, the terms can be expressed as: - First term: \( a \) - Third term: \( b = a + 2d \) ...
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