How do you identity if the equation x^2+4y^2+2x-24y+33=0x2+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 -

x^2+4y^2+2x-24y+33=0x2+4y2+2x24y+33=0

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

ax^2+cy^2+dx+ey+f=0ax2+cy2+dx+ey+f=0

The apply the following conditions to identify the equation.

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

In our case

a=1; c=4a=1;c=4

1 xx 4 = 4 >01×4=4>0, then the given equation is ellipse.