Consider the equation. $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$
Explain how to identify the graph of the equation.

A)Find the discriminant of the equation to identify the graph of the equation.
B)Find the foci of the equation to identify the graph of the equation.
C)Find the major axis of the equation to identify the graph of the equation.
D)Find the minor axis of the equation to identify the graph of the equation.
E)Find the vertices of the equation to identify the graph of the equation.

Question

Consider the equation.  $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$ 
Explain how to identify the graph of the equation.

A)Find the discriminant of the equation to identify the graph of the equation.
B)Find the foci of the equation to identify the graph of the equation.
C)Find the major axis of the equation to identify the graph of the equation.
D)Find the minor axis of the equation to identify the graph of the equation.
E)Find the vertices of the equation to identify the graph of the equation.

Quizplus · Accepted Answer

The discriminant of a quadratic equation helps determine the nature of its roots and, by extension, the shape of its graph. For conic sections, analyzing coefficients and their relationships can indicate the type of graph (ellipse, hyperbola, etc.), but the discriminant specifically applies to quadratic equations, not directly to identifying the graph of conic sections. However, understanding the structure of the equation can hint at the type of conic section it represents.

Consider the Equation 10x2−5xy+10y2−81=010 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 010x2−5xy+10y2−81=0

Consider the Equation $10 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 81 = 0$