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If the sum of slopes of the lines given ...

If the sum of slopes of the lines given by `4x^2+2kxy-7y^2=0` is equal to the product of slopes , then k is equal to

A

`-4`

B

`4`

C

`-2`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `y_1=m_1x and y=m_2x` be the lines given by `4x^2+2kxy-7y^2=0`. Then ,
`m_1+m_2=(-2h)/(b)=(-2k)/(-7)=(2k)/(7) and m_1m_2=(a)/(b)=(-4)/(7)`
It is given that `m_1+m_2=m_1m_2`
`rArr (2k)/(7)=(-4)/(7)rArr k=-2`
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