Classify the graph of the equation below as a circle, a parabola, an ellipse, or a hyperbola.
$$2 x ^ { 2 } + 5 y ^ { 2 } + 8 x - 2 y = 0$$
A) ellipse
B) hyperbola
C) parabola
D) circle

Question

Quizplus · Accepted Answer

The equation can be rewritten as:
$$2(x+2)^2+5(y-1)^2=9$$
Dividing by 9, we get:
$$\frac{(x+2)^2}{\left(\frac{3}{\sqrt{2}}\right)^2}+\frac{(y-1)^2}{\left(\frac{3}{\sqrt{5}}\right)^2}=1$$
This is the equation of an ellipse centered at $(-2,1)$ with semi-major axis $\frac{3}{\sqrt{2}}$ and semi-minor axis $\frac{3}{\sqrt{5}}$. Therefore, the graph is an ellipse.

Classify the Graph of the Equation Below as a Circle 2x2+5y2+8x−2y=02 x ^ { 2 } + 5 y ^ { 2 } + 8 x - 2 y = 02x2+5y2+8x−2y=0

Classify the Graph of the Equation Below as a Circle $2 x ^ { 2 } + 5 y ^ { 2 } + 8 x - 2 y = 0$