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

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Question

(C) The given equation is $ax^2 + 4xy + y^2 = 0$. Let the slopes of the two lines be $m$ and $3m$.Comparing the equation with $Ax^2 + 2Hxy + By^2 = 0$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The given equation is $ax^2 + 4xy + y^2 = 0$. Let the slopes of the two lines be $m$ and $3m$.Comparing the equation with $Ax^2 + 2Hxy + By^2 = 0$,we have $A = a$,$2H = 4$ (so $H = 2$),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 $3(-1)^2 = a$,which implies $a = 3$.Thus,the correct option is $C$.

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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