Q81 / 150 · MHT CET 2021 (20 Sep Shift 2) · Mathematics

If the equation $3 x^2-k x y-3 y^2=0$ represents the bisectors of angles between the lines $x^2-3 x y-4 y^2=0$, then value of $k$ is

  • A
    -6
  • Correct answer
    B
    -10
  • C
    6
  • D
    10

Solution

We have $x^2-3 x y-4 y^2=0$ and comparing it with standard equation, we write $$ \mathrm{A}=1, \mathrm{H}=\frac{-3}{2}, \mathrm{~B}=-4 $$ Equation of bisector of angle of this line is $$ \begin{aligned} & \frac{x^2-y^2}{A-B}=\frac{x y}{H} \Rightarrow \frac{x^2-y^2}{1+4}=\frac{x y}{\left(\frac{-3}{2}\right)} \\ & \therefore-3 x^2+3 y^2=10 x y \Rightarrow 3 x^2+10 x y-3 y^2=0 \end{aligned} $$ Comparing with given equation, we get $\mathrm{k}=-10$

Hence, the correct answer is option: 'B'.

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