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?

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Answer 1 · 2016-12-04T05:59:18

The given equation represents ellipses.

Watch this general form of an equation of conic section -

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

If #A xx C=1#; It is a circle.

If #A xx C > 0#; It is a ellips.

If #A xx C<1#; It is a Hyperbola.

If #A# or #B# is equal to zero, it is a parabola.

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 #A xx C# i.e., #1 xx 4 >0#

The given equation represents ellipses.