Use the discriminant to classify the graph. $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$
A)The graph is a cone.
B)The graph is a parabola.
C)The graph is a ellipse or circle.
D)The graph is a hyperbola.
E)The graph is a line.

Question

Use the discriminant to classify the graph.​ $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$ ​
A)The graph is a cone.
B)The graph is a parabola.
C)The graph is a ellipse or circle.
D)The graph is a hyperbola.
E)The graph is a line.

Quizplus · Accepted Answer

The given equation is a second-degree equation in two variables, x and y. To classify the graph of such an equation, we can use the discriminant $D = B^2 - 4AC$, where A, B, and C are the coefficients of $x^2$, $xy$, and $y^2$ respectively. In this case, A = 1 (coefficient of $x^2$), B = 1 (coefficient of $xy$), and C = 10 (coefficient of $y^2$). Plugging these into the discriminant formula gives $D = 1^2 - 4(1)(10) = 1 - 40 = -39$. Since the discriminant is negative, the graph represents an ellipse or a circle.

Use the Discriminant to Classify the Graph x2+xy+10y2+x+y−10=0x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0x2+xy+10y2+x+y−10=0

Use the Discriminant to Classify the Graph $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$