Question

Use the discriminant to determine whether the graph of this equation is a parabola, an ellipse, or a hyperbola: 5 x²+4 x y+2 y²=18

Answer 1

The graph of the equation is a hyperbola.

Step-by-step explanation:

The given equation is 5x² + 4xy + 2y² = 18. To determine the shape of the graph, we can use the discriminant. The discriminant can be found by evaluating the expression b² - 4ac, where a, b, and c are the coefficients of the equation in the form ax² + bxy + cy² = 0.

In this case, the equation is 5x² + 4xy + 2y² - 18 = 0, so the coefficients are a = 5, b = 4, and c = 2. Calculating the discriminant, we have 4² - 4(5)(2) = 16 - 40 = -24.

Since the discriminant is negative (-24), the graph of the equation is a hyperbola.