TS EAMCET · Maths · Straight Lines
For \(a \neq b \neq c\), if the lines \(x+2 a y+a=0\), \(x+3 b y+b=0\) and \(x+4 c y+c=0\) are concurrent, then \(a, b, c\) are in
- A Arithmetic progression
- B Geometric progression
- C Harmonic progression
- D Arithmetico geometric progression
Answer & Solution
Correct Answer
(C) Harmonic progression
Step-by-step Solution
Detailed explanation
Lines \[ \begin{aligned} & x+2 a y+a=0 \\ & x+3 b y+b=0 \end{aligned} \] and \(x+4 c y+c=0\) are concurrent. If \(\left|\begin{array}{lll}1 & 2 a & a \\ 1 & 3 b & b \\ 1 & 4 c & c\end{array}\right|=0\) Applying \(R_1 \rightarrow R_1-R_2, R_2 \rightarrow R_2-R_3\), we get…
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