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  • For the second degree equation <img alt="\mathrm{a x^2+2 h x y+b y^2+2 g x+2 f y+c}=0" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Ba%20x%5E2&plus;2%20h%20x%20y&plu

For the second degree equation \mathrm{a x^2+2 h x y+b y^2+2 g x+2 f y+c}=0 which one is not true? 
 

Option: 1

\mathrm {Represents \: \: a\: \: circle\: \: if \: \: a=b and \left|\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right|=\Delta=0, h=0}
 


Option: 2

\mathrm{Represent\: \: an\: \: ellipse\: \: if \: \: \Delta \neq 0 \: \: and \: \: h^2<a b}


Option: 3

\mathrm {\text {Represent a hyperbola if }\Delta \neq 0 \: \: and \: \: h^2>a b}


Option: 4

\mathrm {\text{Represent a parabola if }\Delta \neq 0 \: \: and\: \: h^2=a b}


Answers (1)

best_answer

The second degree equation  \mathrm {a x^2+2 h x y+b y^2+2 g x+ 2 f y+c}=0

represent a circle if  \mathrm {a=b, h=0} and \mathrm \Delta \neq 0, the equation represent a parabola if

\mathrm {\Delta \neq 0\: \: and \: \: h^2=a b,}  and it represent an ellipse if  \mathrm {\Delta \neq 0 \: \: \&\: \: h^2<a b}

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