The equation ,[tex]-2x^2+5xy-7y^2+9x-7y+13=0[/tex] represents a conic. The discriminant is is -31 , so the represents an ellipse .
A curve obtained by a cone and a plane is called conic .
Here given equation is
[tex]-2x^2+5xy-7y^2+9x-7y+13=0[/tex]
we know that discriminants of equation
[tex]$A x^{2}+B x y+C y^{2}+D x+E y+F=0$[/tex]
is [tex]$D=B^{2}-4 A C$[/tex]
and if
D<0 it's ellipse
D=0 it's parabola
D>0 It's hyperbola
Here, the is
[tex]$D=5^{2}-4(-2)(-7)=-31$[/tex]
Hence it's an ellipse
The equation ,[tex]-2x^2+5xy-7y^2+9x-7y+13=0[/tex] represents a conic. The discriminant is is -31 , so the represents an ellipse .
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