# 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?

##### 2 Answers

Nov 9, 2016

Circle

#### Explanation:

Modify the equation by completing the square for

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

The equation above describes a circle of radius

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

Nov 9, 2016

the eqn of a circle is

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

note;

1) the coefficients of

2) there are no

Ellipses are of the form

hyperbolas are of the form

again no