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  4. If ax2 + 4xy + y2 + ax + 3y + 2 = 0 represents a parabola, then a is

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Q. If $ ax^2 + 4xy + y^2 + ax + 3y + 2 = 0 $ represents a parabola, then $ a $ is

AMUAMU 2010

Solution:

Given, $ax^{2}+4xy+y^{2}+ax+3y+2=0$
Since, the given equation represent a parabola, then it satisfies, $H^{2}=AB \dots(i)$
On comparing with,
$Ax^{2}+2Hxy+By^{2}+2gx+2fy+c=0$
Then, $A=a, B=1$
and $H=2$
From Eq. (i), $(2)^{2}=(a) (1)$,
$a=4$