# 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?

Nov 9, 2016

Circle

#### Explanation:

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

${x}^{2} + {\left(y - 4\right)}^{2} = 5$

The equation above describes a circle of radius $\sqrt{5}$ centered at $\left(0 , 4\right)$.

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

Nov 9, 2016

the eqn of a circle is ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} + {r}^{2}$

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

${x}^{2} + {y}^{2} + f x + g y + h = 0$

note;

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

2) there are no $' x y '$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 $' x y '$terms.