Respuesta :

Conics have the following general form:

[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]

For our given conic, we have the following:

[tex]A=2,B=9,C=14,D=E=0,F=-5[/tex]

To identify our conic, we need to calculate the discriminant

[tex]B^2-4AC[/tex]

If the discriminant is less than zero, the conic section is an ellipse;

If the discriminant is equal to zero, the conic section is a parabola;

If the discriminant is equal to zero, the conic section is a hyperbola

Now, calculating the discriminant:

[tex]9^2-4\times2\times14=81-112=-31[/tex]

Since the discriminant is negative, this conic section is an ellipse.

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