Question

The conic represented by $y^2-4x-4y+\lambda =0$

• A. A parabola $\forall \lambda \in R$
• B. $e=1$ when $\lambda =2020$
• C. an ellipse if $\lambda <0$
• D. A non-degenerate conic

Answer 1

Answer: (A), (B), (D)

The correct options are
A A parabola $\forall \lambda \in R$
B $e=1$ when $\lambda =2020$
D A non-degenerate conic

$y^2-4x-4y+\lambda =0$
On comparing with

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

We have , $a=0,h=0,b=1,g=-2,f=-2,c=\lambda$

$\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2=-1\ne 0$

also $h^2=ab$
Hence conic will be a parabola and for parabola $e=1$
its alos termed as non-degenerate conic.