Identify the graph of the equation using the discriminant. 4x² - 10xy + 5y² - 4x + 2y - 3 = 0 A) parabola B) circle or ellipse C) hyperbola

Question

Quizplus · Accepted Answer

The given equation is a second-degree equation in two variables, x and y. To identify the graph of such an equation, we can use the discriminant of the conic section, $B^2 - 4AC$, where $A$, $B$, and $C$ are the coefficients of $x^2$, $xy$, and $y^2$ respectively. In this equation, $A = 4$, $B = -10$, and $C = 5$. Plugging these into the discriminant formula gives $(-10)^2 - 4(4)(5) = 100 - 80 = 20$, which is positive. A positive discriminant indicates that the graph is a hyperbola.

Identify the Graph of the Equation Using the Discriminant