# How do you identity if the equation x^2+y^2-8x-6y+5=0 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

Nov 2, 2016

The equation represents a circle of center $\left(4 , 3\right)$ and radius $\sqrt{20}$

#### Explanation:

Let's rewrite the equation and complete the square
${x}^{2} - 8 x + {y}^{2} - 6 y = - 5$
${x}^{2} - 8 x + 16 + {y}^{2} - 6 y + 9 = - 5 + 16 + 9$
${\left(x - 4\right)}^{2} + {\left(y - 3\right)}^{2} = 20$
${\left(x - 4\right)}^{2} + {\left(y - 3\right)}^{2} = {\left(\sqrt{20}\right)}^{2}$
this is the equation of a circle, the center is $\left(4 , 3\right)$
and the radius is $\sqrt{20}$
You draw a circle, center(4,3) and radius $4.5$
graph{(x-4)^2+(y-3)^2=20 [-9.46, 13.04, -1.88, 9.37]}