Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola.
$$64 x ^ { 2 } + 64 y ^ { 2 } + 192 x + 24 y - 327 = 0$$
A) hyperbola
B) ellipse
C) circle
D) parabola

Question

Quizplus · Accepted Answer

Rearranging the given equation, we get:
$$(x+3)^2 + (y-\frac{5}{2})^2 = \frac{327}{64}+1$$
This equation is in the standard form of a circle:
$$(x-a)^2 + (y-b)^2 = r^2$$
where $a=-3$, $b=\frac{5}{2}$, and $r=\sqrt{\frac{327}{64}+1}$. Therefore, the graph is a circle.

Classify the Graph of the Equation Below as a Circle 64x2+64y2+192x+24y−327=064 x ^ { 2 } + 64 y ^ { 2 } + 192 x + 24 y - 327 = 064x2+64y2+192x+24y−327=0

Classify the Graph of the Equation Below as a Circle $64 x ^ { 2 } + 64 y ^ { 2 } + 192 x + 24 y - 327 = 0$