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If slopes of lines represented by K x^{2}+5 x y+y^{2}=0 differ by 1 then K=
(A) 2
(B) 3
(C) 6
(D) 8
maths | Maths
If slopes of lines represented by K x^{2}+5 x y+y^{2}=0 differ by 1 then K=
(A) 2
(B) 3
(C) 6
(D) 8

Correct option is

(C) 6

\mathrm{Kx}^{2}+5 \mathrm{xy}+\mathrm{y}^{2}=0

\mathrm{m}_{1}+\mathrm{m}_{2}=-5, \mathrm{~m}_{1} \mathrm{~m}_{2}=\mathrm{K}

Also, \mathrm{m}_{1}-\mathrm{m}_{2}=1…… [Given]

Now,

\left(\mathrm{m}_{1}-\mathrm{m}_{2}\right)^{2}=\left(\mathrm{m}_{1}+\mathrm{m}_{2}\right)^{2}-4 \mathrm{~m}_{1} \mathrm{~m}_{2} \Rightarrow 1=25-4 \mathrm{~K} \Rightarrow \mathrm{K}=6

i

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