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AP EAMCET · Maths · Straight Lines

If three non-zero real numbers \(a, b, c\) are in harmonic progression, then the straight lines \(\frac{x}{a}+\frac{y}{b}-\frac{2}{c}=0\) are concurrent at the point

  1. A \((1,-2)\)
  2. B \((-2,4)\)
  3. C \((4,-2)\)
  4. D \((-2,-4)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((-2,4)\)

Step-by-step Solution

Detailed explanation

\(\frac{2}{b} = \frac{1}{a} + \frac{1}{c}\) \(\frac{x}{a} + y\left(\frac{1}{2a} + \frac{1}{2c}\right) - \frac{2}{c} = 0\) \(\left(x+\frac{y}{2}\right)\frac{1}{a} + \left(\frac{y}{2}-2\right)\frac{1}{c} = 0\) \(x+\frac{y}{2}=0\) \(\frac{y}{2}-2=0 \implies y=4\)…