Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola.
$$y ^ { 2 } + 13 x + y - 79 = 0$$
A) ellipse
B) parabola
C) hyperbola
D) circle

Question

Quizplus · Accepted Answer

The given equation is not in a standard form of any conic section. We can try to complete the square to rewrite the equation in a standard form, but that will not lead to any of the standard forms of a circle, parabola, ellipse, or hyperbola. Therefore, we can conclude that the graph of the equation is not a conic section and is not one of the choices given. However, we can notice that the highest power of $x$ is a first degree term and the highest power of $y$ is a second degree term. This suggests that the graph is a parabola.

Classify the Graph of the Equation Below as a Circle y2+13x+y−79=0y ^ { 2 } + 13 x + y - 79 = 0y2+13x+y−79=0

Classify the Graph of the Equation Below as a Circle $y ^ { 2 } + 13 x + y - 79 = 0$