If the slope of one line of ax^2+4xy+y^2=0 is | vedclass

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(C) Let the slopes of the lines be $m$ and $3m$ respectively,which are represented by the equation $ax^2+4xy+y^2=0$.Comparing with $Ax^2+2Hxy+By^2=0$,

Vedclass · Accepted Answer

$3$

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(C) Let the slopes of the lines be $m$ and $3m$ respectively,which are represented by the equation $ax^2+4xy+y^2=0$.Comparing with $Ax^2+2Hxy+By^2=0$,we have $A=a$,$2H=4 \Rightarrow H=2$,and $B=1$.The sum of the slopes is $m+3m = -\frac{2H}{B} = -\frac{4}{1} = -4$.$4m = -4 \Rightarrow m = -1$.The product of the slopes is $m(3m) = \frac{A}{B} = \frac{a}{1} = a$.$3m^2 = a$.Substituting $m = -1$,we get $3(-1)^2 = a \Rightarrow a = 3$.Hence,option $C$ is correct.

If the slope of one line of $ax^2+4xy+y^2=0$ is $3$ times the other,then the value of '$a$' is

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