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COMEDK · Maths · 10. Straight Lines

A straight line passes through the point \(P(\log_2 16 , \log_3 27)\) such that the portion of the line intercepted between the co-ordinate axes is divided by \(P\) in the ratio \(1:2\) internally (starting from the \(x\)-axis). Then the equation of the line is:

  1. A \(x + y - 7 = 0\)
  2. B \(3x + 2y - 18 = 0\)
  3. C \(3x + 4y - 24 = 0\)
  4. D \(x + 2y - 10 = 0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(3x + 2y - 18 = 0\)

Step-by-step Solution

Detailed explanation

The coordinates of the point \(P\) are given by \((\log_2 16, \log_3 27)\). Since \(\log_2 16 = \log_2 (2^4) = 4\) and \(\log_3 27 = \log_3 (3^3) = 3\), the point is \(P(4, 3)\). Let the line intersect the \(x\)-axis at \(A(a, 0)\) and the \(y\)-axis at \(B(0, b)\). It is given…