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
- A \(x^{-1}+y^{-1}=2\)
- B \(2 x^{-1}+y^{-1}=1\)
- C \(x^{-1}+2 y^{-1}=1\)
- D \(2 x^{-1}+3 y^{-1}=1\)
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…
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