Question

What is the center and radius of -10x = -121 - y2 - x2 -22y

Answer 1

We need to find the center and the radius of

$-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y$

The general circle equation is the following

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center and

r is the radius

1. rearrange the equation

$(x^2-10x)+(y^2+22y+121)=0$

2. Add 25 on both sides

$(x^2-10x+25)+(y^2+22y+121)=25$

3. Factor

$(x-5)^2+(y+11)^2=5^2$

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5