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TS EAMCET · Maths · Straight Lines

If a line \(L\) passes through the point of intersection of the lines \(2 x+3 y+1=0\) and \(x+y-3=0\) and the angle made by the line \(L\) with \(X\)-axis measured in positive direction from the positive \(X\)-axis is \(\tan ^{-1} \frac{2}{3}\), then the sum of the intercepts made by this line on the axes is

  1. A \(\frac{-1}{41}\)
  2. B \(\frac{205}{6}\)
  3. C \(\frac{5}{41}\)
  4. D \(\frac{41}{6}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{41}{6}\)

Step-by-step Solution

Detailed explanation

Let equation of required line is \(\frac{x}{a}+\frac{y}{b}=1\) ...(i) Since, Eq. (i) passes through \((10,-7)\) which is point of intersection of given lines. So, \(\frac{10}{a}-\frac{7}{b}=1\) Also given, slope…