NIMCET 2016 Question Paper with solutions

Question : 86 of 120

Marks: +1, -0

If the sum of the slopes of the lines given by

x^2

– 2cxy –

7y^2

= 0 is four times their product, then the value of ‘c’ is;

Solution:

Given equation of lines is

x^2-2cxy-7y^2=0

..(i)
Let the

m_1

and

m_2

be the slopes of Eq. (i), then

m_1+m_2=-{2c}/7

and

m_1m_2=-1/7

According to given condition,

m_{1}+m_{2}=4m_{1}m_{2}

⇒\;\;{-2c}/{7}=4(-\;\;{1}/{7})

⇒-\;\;{2c}/{7}=-\;\;{4}/{7}

⇒2c=4

⇒c=2

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