Question

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?

Answer 1

The equation represents a circle of center `(4,3)` and radius `sqrt20`

Explanation:

Let's rewrite the equation and complete the square
`x^2-8x+y^2-6y=-5`
`x^2-8x+16+y^2-6y+9=-5+16+9`
`(x-4)^2+(y-3)^2=20`
`(x-4)^2+(y-3)^2=(sqrt20)^2`
this is the equation of a circle, the center is `(4,3)`
and the radius is `sqrt20`
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]}