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  4. If the sum of the slopes of the lines given by 4 x2+2 λ x y-7 y2=0 is equal to the product of the slopes, then λ is equal to

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Q. 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

AP EAMCETAP EAMCET 2020

Solution:

$4 x^{2}+2 \lambda x y-7 y^{2}=0$
$a=4,2 h=2 \lambda, b=-7$
Given, sum of slopers = product of slopers
$m_{1}+m_{2}=m_{1} m_{2}$
$\frac{-2 h}{b}=\frac{a}{b}$
$\frac{-2 \lambda}{-7}=\frac{4}{-7}$
$\lambda=-2$