Identify the equation without applying a rotation of axes.
-$$3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$$
A) parabola
B) hyperbola
C) ellipse
D) not a conic

Question

Quizplus · Accepted Answer

The given equation is a general second-degree equation in x and y. To determine the type of conic, we calculate the discriminant $ B^2 - 4AC $, where A, B, and C are the coefficients of $ x^2 $, $ xy $, and $ y^2 $ respectively. Here, A = 3, B = 8, and C = 2. The discriminant is $ 8^2 - 4(3)(2) = 64 - 24 = 40 $. Since the discriminant is positive, the conic is a hyperbola.

Identify the Equation Without Applying a Rotation of Axes 3x2+8xy+2y2+3x+2y+10=03 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 03x2+8xy+2y2+3x+2y+10=0

Identify the Equation Without Applying a Rotation of Axes $3 x ^ { 2 } + 8 x y + 2 y ^ { 2 } + 3 x + 2 y + 10 = 0$