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 $y^2 - 4x^2 + 4x - 8y - 24 = 0$, which is a hyperbola because it has terms in $x^2$ and $y^2$ with opposite signs, indicating a hyperbolic shape.

Select the Graph of the Equation as a Circle, a Parabola