# How do you identity if the equation #x^2+4y^2-11=2(4y-x)# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

Dec 4, 2016

The given equation represents ellipses.

#### Explanation:

Watch this general form of an equation of conic section -

#Ax^2+Bx+Cy^2+Dx+Ey+F=0#

If

If

If

If

Our equation is -

#x^2 +4y^2-11=2(4y-x)#

Let us rewrite it in the know form to identify the equation.

#x^2 +4y^2-11=8y-2x#

#x^2+2x+4y^2-8y-11 =0#

#A= 1#

#C=4#

Since

The given equation represents ellipses.