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TS EAMCET · Maths · Straight Lines

A straight line passing through a point \((3,2)\) cuts X and Y -axes at the points A and B respectively. If a point P divides AB in the ratio \(2: 3\), then the equation of the locus of point P is

  1. A \(\frac{9}{x}+\frac{4}{y}=1\)
  2. B \(9 x+4 y=5 x y\)
  3. C \(4 x+9 y=5 x y\)
  4. D \(\frac{4}{x}+\frac{9}{y}=1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(4 x+9 y=5 x y\)

Step-by-step Solution

Detailed explanation

Let the equation of the line be \(\frac{x}{a} + \frac{y}{b} = 1\). Point A is \((a,0)\) and point B is \((0,b)\). Point P \((x,y)\) divides AB in ratio \(2:3\): \(x = \frac{3a + 2(0)}{2+3} = \frac{3a}{5} \implies a = \frac{5x}{3}\)…