If the sum of the slopes of the lines given by `4x^2+2lambdaxy-7y^2=4` is equal to the product of the slopes,then `lambda` is equal to?

If the sum of the slopes of the lines given by `4x^2+2lambdaxy-7y^2=4`

1.	If the sum of the slopes of the lines given by `4x^2+2lambdaxy-7y^2=4` is equal to the product of the slopes,then `lambda` is equal to?
Answer» Let we have below two lines that represent the given equation. `y-m_1x = 0` and `y-m_2x=0` Combined equation of these two lines will be, `(y-m_1x)(y-m_2x) = 0` `y^2-(m_1+m_2)xy+m_1m_2x^2=0->(1)` Now, the given equation is, `4x^2+2lambdaxy -7y^2= 4` `y^2-4/7x^2- 2/7lambdaxy = 0` Comparing this with the given equation (1), `m_1+m_2 = 2/7lambda` `m_1m_2 = -4/7` As we are given sum and product of roots are equal. So, `2/7lambda = -4/7=> lambda = -2`

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If the sum of the slopes of the lines given by `4x^2+2lambdaxy-7y^2=4` is equal to the product of the slopes,then `lambda` is equal to?

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