How do you identity if the equation #x^2-8y+y^2+11=0# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

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Answer 1 · 2016-11-09T07:16:46

Circle

Modify the equation by completing the square for #y#.

#x^2 + (y-4)^2 = 5#

The equation above describes a circle of radius #sqrt5# centered at #(0,4)#.

graph{x^2 + (y-4)^2 = 5 [-9.67, 10.33, -1.6, 8.4]}

Answer 2 · 2016-11-09T09:07:22

the eqn of a circle is #(x-a)^2+(y-b)^2+r^2#

when multiplied and simplified out the eqn can be rearranged to the form

#x^2+y^2+fx+gy+h=0#

note;

1) the coefficients of #x# &#y# are the same.

2) there are no #'xy' #terms

Ellipses are of the form

#x^2/a+y^2/b=1#

hyperbolas are of the form

#x^2/a-y^2/b=1#

again no #'xy' #terms.