Identify the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$
A)Circle
B)Hyperbola
C)Ellipse
D)Parabola
E)None of the above

Question

Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.  $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$ 
A)Circle
B)Hyperbola
C)Ellipse
D)Parabola
E)None of the above

Quizplus · Accepted Answer

This equation represents a hyperbola because it has terms in $x^2$ and $y^2$ with opposite signs, indicating a hyperbola. Specifically, the coefficients of $x^2$ and $y^2$ are equal in magnitude but opposite in sign ($3x^2 - 3y^2$), which is characteristic of a hyperbola.

Identify the Equation as a Circle, a Parabola, an Ellipse 3x2−3y2−3x+6y+17=03 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 03x2−3y2−3x+6y+17=0

Identify the Equation as a Circle, a Parabola, an Ellipse $3 x ^ { 2 } - 3 y ^ { 2 } - 3 x + 6 y + 17 = 0$