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?

1 Answer
Nov 2, 2016

Answer:

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]}