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The equation \mathrm{x^2+4 x y+4 y^2+4 x+4 y+\lambda=0} will represent a parabola
 

Option: 1

 for all values of \lambda
 


Option: 2

 for all except for one value of \lambda
 


Option: 3

 for no values of \lambda
 


Option: 4

 none of these


Answers (1)

best_answer

Discriminant of the given equation \mathrm{\Delta=a b c+2 f g h-a f^2-b g^2-c h^2 }

\mathrm{ =4 \lambda-16-4-16-4 \lambda=-36~ and ~h^2-a b=0 }
So equation represents parabola for all values of \lambda.

Posted by

Gaurav

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