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 equation is not in standard form for any conic section. However, we can complete the square for $y$ to rewrite the equation as $$\left(y+\frac{1}{2}\right)^2=-x^2+\frac{331}{4}.$$ This is the equation of a vertical parabola since the $y$ term is squared and the $x$ term is negative. Therefore, the answer is B) 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 $y ^ { 2 } + 13 x + y - 79 = 0$