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AP EAMCET · Maths · Straight Lines

A line passing through \(P(4,2)\) cuts the coordinate axes at \(A\) and \(B\) respectively. If \(O\) is the origin, then the locus of the centre of the circum-circle of \(\triangle O A B\) is

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

Answer & Solution

Correct Answer

(B) \(2 x^{-1}+y^{-1}=1\)

Step-by-step Solution

Detailed explanation

Let a line cuts the coordinate axes at \(A\) and \(B\) respectively is \(\frac{x}{a}+\frac{y}{b}=1\) ...(i) So, \(A(a, 0)\) and \(B(0, b)\) and line (i) passes through \(P(4,2)\), so \(\frac{4}{a}+\frac{2}{b}=1\) ...(ii) Now, coordinate of centre of the circumcircle of…