Question

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

• A. $-4$
• B. $4$
• C. $0$
• D. None of these

Answer 1

Answer: (B)

$4$

Given equation is $\lambda x^2+4xy+y^2+\lambda x+3y+2=0$

Compairing with

$a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$

Here $a=\lambda ,b=1,h=2$

For given equation to be an equation of a parabola we must have $h^2=ab$

$\Rightarrow 2^2=1.\lambda$

$\Rightarrow \lambda =4$