Q90 / 160 · TS EAMCET 2021 (06 Aug Shift 2) · Mathematics

If an angular bisector of the coordinate axes is one of the lines of $x^2+2 a x y+3 y^2=0$, then sum of all possible values of $a$ is

  • A
    -1
  • B
    1
  • Correct answer
    C
    0
  • D
    -2

Solution

Bisectors of the angle between the coordinate axes are $y= \pm x$ Then, $x^2+2 a x( \pm x)+3 x^2=0$ $\begin{array}{ll} \Rightarrow & 1 \pm 2 a+3=0 \Rightarrow \pm 2 a=-4 \\ \Rightarrow & \quad a=\frac{-4}{2}, \frac{-4}{-2} \Rightarrow a=-2,2 \\ \therefore & \text { Sum }=0 \end{array}$

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

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