Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. $$y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$$
A)Hyperbola
B)Parabola
C)Circle
D)Ellipse
E)None of the above

Question

Select the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.​ $$y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$$ ​
A)Hyperbola
B)Parabola
C)Circle
D)Ellipse
E)None of the above

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + By^2 + Cx + Dy + E = 0$, where $A$ and $B$ have opposite signs. This indicates that the graph is a hyperbola, as hyperbolas are characterized by the difference of squares (i.e., one squared term is subtracted from another).

Select the Graph of the Equation as a Circle,a Parabola,an y2−4x2+4x−8y−24=0y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0y2−4x2+4x−8y−24=0

Select the Graph of the Equation as a Circle,a Parabola,an $y ^ { 2 } - 4 x ^ { 2 } + 4 x - 8 y - 24 = 0$