Identify the equation without applying a rotation of axes.
-$$4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$$
A) hyperbola
B) ellipse
C) parabola
D) not a conic

Question

Quizplus · Accepted Answer

The discriminant of the conic section, given by $B^2 - 4AC$, is used to identify the type of conic. For the equation $4x^2 + 5xy + 2y^2 + 2x + 3y - 5 = 0$, $A = 4$, $B = 5$, and $C = 2$. The discriminant is $5^2 - 4 \times 4 \times 2 = 25 - 32 = -7$, which is less than zero, indicating an ellipse.

Identify the Equation Without Applying a Rotation of Axes 4x2+5xy+2y2+2x+3y−5=04 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 04x2+5xy+2y2+2x+3y−5=0

Identify the Equation Without Applying a Rotation of Axes $4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$