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The equation \mathrm{x^2-2 x y+y^2+3 x+2=0 } represents 

Option: 1

A parabola

 


Option: 2

An  ellipse


Option: 3

A hyperbola


Option: 4

A circle 


Answers (1)

best_answer

Comparing the given equation with  \mathrm{ax^2+2 h x y+b y^2+2 g x+2 f y+c=0}

Here, \mathrm{a=1, b=1, h=-1, \quad g=\frac{3}{2}, f=0, c=2}

Now \mathrm{\Delta=a b c+2 f g h-a f^2-b g^2-c h^2}

\mathrm{\Rightarrow \Delta=(1)(1)(2)+2\left(\frac{3}{2}\right)(0)(-1)-(1)(0)^2-1\left(\frac{3}{2}\right)^2-2(-1)^2 \Rightarrow \Delta=\frac{-9}{4} \text { i.e., } \Delta \neq 0 \text { and } h^2-a b=1-1=0}

\mathrm{\text { i.e., } h^2=a b}

So given equation represents a parabola.

 

Posted by

Sanket Gandhi

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