Final answer:
The equation represents a conic section, and using the discriminant, which is positive, it can be determined that the graph of the equation is an ellipse.
Step-by-step explanation:
The equation 11x² - 24xy + 4y² + 20 = 0 represents a conic section, and we can use the discriminant to determine its specific type. In general, for a second-degree equation in x and y of the form Ax² + Bxy + Cy² + Dx + Ey + F = 0, the discriminant (D) is given by B² - 4AC. For this equation, A = 11, B = -24, and C = 4. Plugging these into the discriminant formula gives us D = (-24)² - 4(11)(4) = 576 - 176 = 400.
Since the discriminant is positive (D > 0), and since A and C are the same sign (both positive), the graph of the equation is an ellipse. If the discriminant were zero, it would be a parabola, and if A and C had opposite signs, it would be a hyperbola.