Q85 / 160 · AP EAMCET 2024 (20 May Shift 1) · Mathematics

If the slope of one line of the pair of lines $2 x^2+h x y+6 y^2$ $=0$ is thrice the slone of the other line, then $\mathrm{h}=$

  • A
    $\pm 16$
  • B
    $\pm 9$
  • C
    $\pm 18$
  • Correct answer
    D
    $\pm 8$

Solution

$2 x^2+h x y+6 y^2=0$ Comparing with $a x^2+2 h x y+b y^2=0$ $a=4, b=12$ Let $m_1$ and $m_2$ be the slopes We know, $m_1 m_2=\frac{a}{b}=\frac{1}{3}$ Also $m_1=3 m_2 \Rightarrow 3 m_1^2=\frac{1}{3} \Rightarrow m_1= \pm \frac{1}{3}$ And $m_1+m_2=-\frac{2 h}{b} \Rightarrow 4 m_1=\frac{-2 h}{12} \Rightarrow h= \pm 8$

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

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