Q106 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

If the sum of the slopes of the lines given by \(4 x^2+2 \lambda x y-7 y^2=0\) is equal to the product of the slopes, then \(\lambda\) is equal to

  • A
    -4
  • B
    4
  • Correct answer
    C
    -2
  • D
    2

Solution

\(\begin{aligned} & 4 x^2+2 \lambda x y-7 y^2=0 \\ & a=4,2 h=2 \lambda, b=-7 \end{aligned}\) Given, sum of slopers = product of slopers \(\begin{aligned} m_1+m_2 & =m_1 m_2 \\ \frac{-2 h}{b} & =\frac{a}{b} \\ \frac{-2 \lambda}{-7} & =\frac{4}{-7} \\ \lambda & =-2 \end{aligned}\) Hence, option (c) is correct.

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

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