JEE Mains · Maths · STD 11 - 9. straight line
A straight the through a fixed point \((2, 3)\) intersects the coordinate axes at distinct points \(P\) and \(Q.\) If \(O\) is the origin and the rectangle \(OPRQ\) is completed, then the locus of \(R\) is:
- A \(2x + 3y = xy\)
- B \(3x + 2y = xy\)
- C \(3x + 2y = 6xy\)
- D \(3x + 2y = 6\).
Answer & Solution
Correct Answer
(B) \(3x + 2y = xy\)
Step-by-step Solution
Detailed explanation
Equation of \(PQ\) is \(\frac{x}{h} + \frac{y}{k} = 1\,\,\,\,\,\,\,......\left( 1 \right)\) Since, \((1)\) passes through the fixed point \((2,3)\) Then, \(\frac{2}{h} + \frac{3}{k} = 1\,\) Then, the locus of \(R\) is \(\frac{2}{x} + \frac{3}{y} = 1\) or \(3x + 2y = xy\).
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