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JEE Main 202125 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2021 · 25 July · Evening Shift · Mathematics · Straight Lines

Let the equation of the pair of lines, y = px and y = qx, can be...

Let the equation of the pair of lines, y=pxandy=qx,y = px and y = qx, can be written as \left(y - px\right)\left(y - qx\right) = 0 . Then the equation of the pair of the angle bisectors of the lines x2−4xy−5y2=0{x}^{2} - 4xy - 5{y}^{2} = 0 is:

Options

  1. Ax2−3xy+y2=0{x}^{2} - 3xy + {y}^{2} = 0
  2. Bx2+4xy−y2=0{x}^{2} + 4xy - {y}^{2} = 0
  3. Cx2+3xy−y2=0{x}^{2} + 3xy - {y}^{2} = 0
  4. Dx2−3xy−y2=0{x}^{2} - 3xy - {y}^{2} = 0

Correct answer

C. x2+3xy−y2=0{x}^{2} + 3xy - {y}^{2} = 0

Step-by-step solution

We have, equation of a pair of lines x2−4xy−5y2=0{x}^{2} - 4xy - 5{y}^{2} = 0

Now, equation of bisector of a pair of lines x2−y21−(−5)=xy−2\dfrac{{x}^{2} - {y}^{2}}{1 - \left(- 5\right)} = \dfrac{xy}{- 2}

⇒x2−y26=xy−2⇒ \dfrac{{x}^{2} - {y}^{2}}{6} = \dfrac{xy}{- 2}

⇒x2−y2=−3xy⇒ {x}^{2} - {y}^{2} = - 3xy

⇒x2+3xy−y2=0.⇒ {x}^{2} + 3xy - {y}^{2} = 0 .

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