# The gradient of one of the straight line in ax^2+2hxy+by^2= 0 is twice that of the other.Then which one of the following is true? (i) 8h^2+9ab=0 (ii)8h^2=9ab (iii)h^2=ab (iv) 3h^2-5ab=0

The gradient of one of the straight line in $a{x}^{2}+2hxy+b{y}^{2}=0$ is twice that of the other.Then which one of the following is true?

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if ${m}_{1}$ & ${m}_{2}$ are 2 slopes for the pairof straight lines $a{x}^{2}+2hxy+b{y}^{2}=0$ then

but ${m}_{2}=2{m}_{1}$
........(1)
$⇒{m}_{1}=-2h/3b$
sub. ${m}_{1}$ in (1) we get $2\left(4{h}^{2}/9{b}^{2}\right)=a/b$
$⇒8{h}^{2}=9ab$
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