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JEE Main 20188 April
Exam
JEE Main
Year
2018
Date
8 April
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2018 · 8 April · Mathematics · Straight Lines

A straight line through a fixed point (2, 3) intersects the...

A straight line through a fixed point (2,3)\left(2, 3\right) intersects the coordinate axes at distinct points PandQP and Q. If OO is the origin and the rectangle OPRQOPRQ is completed, then the locus of RR is:A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q . If O is the

Options

  1. A3x+2y=6xy3x + 2y = 6xy
  2. B3x+2y=63x + 2y = 6
  3. C2x+3y=xy2x + 3y = xy
  4. D3x+2y=xy3x + 2y = xy

Correct answer

D. 3x+2y=xy3x + 2y = xy

Step-by-step solution

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q . If O is the

Let the equation of line be xa+yb=1.......\dfrac{x}{a} + \dfrac{y}{b} = 1 . . . . . . .\left(1\right)

Clearly P(a,0)P\left(a, 0\right) and Q\left(0, b\right). Also h=a,k=bh = a, k = b

Now \left(1\right) passes through \left(2, 3\right)

⇒⇒\dfrac{2}{a} + \dfrac{3}{b} =11

⇒⇒\dfrac{2}{h} + \dfrac{3}{k} =11

Hence, locus is 3x+2y=xy3x + 2y = xy

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