Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$
A)Hyperbola
B)Circle
C)Ellipse
D)Parabola
E)None of the above

Question

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $3 y ^ { 2 } + 3 x ^ { 2 } - 21 x + 34 = 0$ 
A)Hyperbola
B)Circle
C)Ellipse
D)Parabola
E)None of the above

Quizplus · Accepted Answer

The equation $3y^2 + 3x^2 - 21x + 34 = 0$ can be rewritten in a form that clearly shows it represents a circle. Both $x^2$ and $y^2$ terms have the same coefficient (after factoring out the 3), indicating it is a circle, not an ellipse, hyperbola, or parabola.

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