The slopes of the lines given by 12x^{2} + bxy + y^{2} = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

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#### Solution

**(C)**

Given equation is `12x^2+bxy-y^2=0`

Comparing with `Ax^2+2Hxy+By^2=0 ," we get"`

A = 12, 2H = b, B = -1

`m_1+m_2=(-2H)/B=-b/-1=b`

`and m_1m_2=A/B=12/-1=-12`

According to given condition,

`|m_1-m_2|=7`

`(m_1-m_2)^2=49`

`b^2-4(-12)=4`

`b^2=49-48`

`b=+-1`

Concept: Acute Angle Between the Lines

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