A) 0
B) 1
C) 2
D) 4
Correct Answer: D
Solution :
We have the given equation \[\lambda {{x}^{2}}+4xy+{{y}^{2}}+\lambda x+3y+2=0\] On comparing this equation with \[a{{x}^{2}}+hxy+b{{y}^{2}}+2gx+2fy+c=0\], we get \[a=\lambda ,h=2,b=1,g=\frac{\lambda }{2},f=\frac{3}{2},c=2\] Since, given equation represents a parabola \[\therefore \] \[{{h}^{2}}=ab\] \[\Rightarrow \] \[4=\lambda \cdot 1\] \[\Rightarrow \] \[\lambda =4\]
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