Q92 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

If slope of one line of \(a x^2+4 x y+y^2=0\) is 3 times the other, then the value of ' \(a\) ' is

  • A
    -3
  • B
    -1
  • Correct answer
    C
    3
  • D
    1

Solution

Let the slope of lines are \(m\) and \(3 m\) respectively which are represented by \(a x^2+4 x y+y^2=0\) \(\because\) Sum of slopes \(=m+3 m=-\frac{4}{1}=-4 \Rightarrow m=-1\) and product of the slopes \(=m(3 m)=\frac{a}{1} \Rightarrow m^2=\frac{a}{3}\) \(\therefore \quad(-1)^2=\frac{a}{3} \Rightarrow a=3\) Hence, option (c) is correct.

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

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