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AP EAMCET · Maths · Straight Lines

A variable line passing through \((l, m)\) intersects the coordinate axes at the points \(A\) and \(B\). If the line drawn parallel to \(Y\)-axis through \(A\) and parallel to \(X\)-axis through \(B\) meet at \(P\), then the locus of \(P\) is

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

Answer & Solution

Correct Answer

(A) \(\frac{l}{x}+\frac{m}{y}=1\)

Step-by-step Solution

Detailed explanation

Let \(O A=a\), and \(O B=b\) Then, the coordinate of a point \(P\) is \((a, b)\). Equation of a variable line \(\frac{x}{a}+\frac{y}{b}=1\) Also the line passes through \((l, m)\) \[ \frac{l}{a}+\frac{m}{b}=1 \] \(\therefore\) The locus of a point \(P\) is…