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?

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Answer 1 · 2016-12-24T05:34:09

The given equation is ellipse.

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

In our case

#a=1; c=4#

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