How do you identity if the equation x2+4y2+2x24y+33=0 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

1 Answer
Dec 24, 2016

The given equation is ellipse.

Explanation:

Given -

x2+4y2+2x24y+33=0

Conic section formula, in the general form, could be written like this-

ax2+cy2+dx+ey+f=0

The apply the following conditions to identify the equation.

If a=c, It is a circle.
If a×c=0, it is a parabola
If a×c>0, it is ellipse .
If a×c<0, it is a hyperbola

In our case

a=1;c=4

1×4=4>0, then the given equation is ellipse.