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

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

#ax^2+cy^2+dx+ey+f=0#

The apply the following conditions to identify the equation.

If

If

If

If

In our case

#a=1; c=4#

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