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If the equation lambdax^2+ 4xy + y^2 + l...

If the equation `lambdax^2+ 4xy + y^2 + lambdax + 3y + 2 = 0` represent a parabola then find `lambda`.

A

-4

B

4

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Comparing the given equation with the general equation of second degree i.e.
`ax^(2)+2hxy+by^(2)+2gx+2fy+c=0`, we have ltbtgt `a-lamda, b=1, c~~2, f=3/2, g=lamda/2 " and "h-2`
`:." "Delta=abc+2fgh-of^(2)-bg^(2)-ch^(2)`
`rArr" "Delta=2lamda=3lamda-(9lamda)/4-(lamda^(2))/4-8=-1/4(lamda^(2)-11lamda+32)`
and, `h^(2)-ab=4-lamda`.
If the given equation represents a parabola, we must have
`Deltaneh^(2)" and "h^(2)=ab`
Clearly, `lamda=4` sarisfies these two conditions.
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