Question

The equation $\lambda x^2+4xy+y^2+\lambda x+3y+2=0$ represents a parabola, if $\lambda$ is

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (D)

We have the given equation
$\lambda x^2+4xy+y^2+\lambda x+3y+2=0$
On comparing this equation with
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$, we get
$a=\lambda ,h=2,b=1,g=\frac{\lambda }{2},f=\frac{3}{2},c=2$
Since, given equation represents a parabola
$\therefore h^2=ab$
$\Rightarrow 4=\lambda \cdot 1$
$\Rightarrow \lambda =4$