# The slopes of the lines given by 12x^2 + bxy + y^2 = 0 differ by 7. Then the value of b is - Mathematics and Statistics

The slopes of the lines given by 12x2 + bxy + y2 = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

#### 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

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