How do you graph x^2 + y^2 - 10x - 10y + 41 = 0?

1 Answer

This is a circle with center at C(5, 5) and with radius=3

Explanation:

from the given
x^2+y^2-10x-10y+41=0
Rearrange the terms then use "Complete the square" method

x^2-10x+y^2-10y=-41
Add 50 on both sides of the equation
(x^2-10x+25)+(y^2-10y+25)=-41+50

(x-5)^2+(y-5)^2=9
We have a circle with Center at (h, k)=(5, 5)
with radius r=3

graph{x^2+y^2-10x-10y+41=0 [-20, 20, -10, 10]}

God bless... I hope the explanation is useful...