Identify the graph of the equation using the discriminant. 10x² + xy + 6y² - 4x + 3y - 6 = 0 A) parabola B) circle or ellipse C) hyperbola

Question

Quizplus · Accepted Answer

To determine the graph using the discriminant, we need to consider the quadratic terms in the equation. In this case, we have 10x^2 + xy + 6y^2, which can be written as the quadratic form Ax^2 + Bxy + Cy^2. 
The discriminant D = B^2 - 4AC is equal to (1)^2 - 4(10)(6) = -239, which is negative. 
Since the discriminant is negative, the graph is a circle or an ellipse. Therefore, the best choice is B.

Identify the Graph of the Equation Using the Discriminant