AP EAMCET · Maths · Straight Lines
A straight line passing through a fixed point \((2,3)\) intersects the coordinate axes at points \(P\) and \(Q\). If \(O\) is the origin and \(R\) is a variable point such that \(O P R Q\) is a rectangle, then the locus of \(R\) is
- A \(3 x+2 y=x y\)
- B \(2 x+3 y=x y\)
- C \(3 x+2 y=6\)
- D \(3 x+2 y=6 x y\)
Answer & Solution
Correct Answer
(A) \(3 x+2 y=x y\)
Step-by-step Solution
Detailed explanation
Equation of line through \( (2,3) \): \( \frac{x}{a} + \frac{y}{b} = 1 \) Using \( (2,3) \): \( \frac{2}{a} + \frac{3}{b} = 1 \) Points of intersection: \( P=(a,0) \), \( Q=(0,b) \) For rectangle \( OPRQ \), the coordinates of \( R \) are \( (a,b) \) Let \( R=(x,y) \). Then…
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