Question

Classify the following conic section from its standard equation: 2x29xy + 14 y2 - 5 = 0

Answer 1

Conics have the following general form:

`Ax^2+Bxy+Cy^2+Dx+Ey+F=0`

For our given conic, we have the following:

`A=2,B=9,C=14,D=E=0,F=-5`

To identify our conic, we need to calculate the discriminant

`B^2-4AC`

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:

`9^2-4*2*14=81-112=-31`

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