# 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?

Dec 24, 2016

The given equation is ellipse.

#### Explanation:

Given -

${x}^{2} + 4 {y}^{2} + 2 x - 24 y + 33 = 0$

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

$a {x}^{2} + c {y}^{2} + \mathrm{dx} + e y + f = 0$

The apply the following conditions to identify the equation.

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

In our case

a=1; c=4

$1 \times 4 = 4 > 0$, then the given equation is ellipse.