Question

x²+2 √3 x y-y²+2=0 Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola.

Answer 1

To determine whether the graph of the equation x²+2√3xy-y²+2=0 is a parabola, ellipse, or hyperbola, we can use the discriminant.

Step-by-step explanation:

To determine whether the graph of the equation x²+2√3xy-y²+2=0 is a parabola, ellipse, or hyperbola, we can use the discriminant. The discriminant is calculated as b²-4ac in a quadratic equation of the form ax²+bx+c=0. In this equation, a=1, b=2√3y, and c=-y²+2.

If the discriminant is positive, the graph represents a parabola. If the discriminant is zero, the graph represents a parabola (degenerate case). If the discriminant is negative, the graph represents an ellipse or a hyperbola.