NIMCET 2016 Question Paper with solutions

Question : 66 of 120

Marks: +1, -0

2x^2 + 7xy + 3y^2

+ 8x + 14y + λ = 0 represents a pair of straight lines, the value of λ is;

Solution:

Given equation of pair of straight line is

2x^2+7\ov{xy}+3y^2+8x+14y+λ=0

...(i)
On comparing Eq. (i) by

ax^2+2hxy+by^2+2gx+2fy+c=0

, we get

a=2,b=3.c=λ,h=7/2,g=4

and

i=7

Eq. (i) will represents a pair of straight line, if

abc+2fgh-af^2-bg^2-ch^2=0

⇒2×3×λ+2×7×4×7/2-2×7^2-3×4^2-λ×(7/2)^2=0

⇒6λ+196-98-48-λ×49/4=0

⇒{24λ-49λ}/4+50=0

⇒{-25λ}/4=200

⇒{-25λ=-200}

λ=8

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