Q84 / 180 · COMEDK 2016 · Mathematics

The lines represented by $a x^{2}+2 h x y+b y^{2}=0$ are perpendicular to each other if

  • A
    $h=0$
  • B
    $h^{2}=a b$
  • Correct answer
    C
    $a+b=0$
  • D
    $h^{2}=a+b$

Solution

We know that the angle between the two lines $a x^{2}+2 h x y+b y^{2}=0$ is given by $\tan \theta=\left|\frac{2 \sqrt{h^{2}-a b}}{a+b}\right|$ $\begin{aligned} \because & \theta &=90^{\circ} \\ & \therefore & a+b &=0 \end{aligned}$

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

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