Find the center (H,K) and radius R of the circle (x^2+y^2-10x+10y+50=49?

Answer 1

(x ² - 10 x) + (y ² + 10 y) = - 1
(x ² - 10 x + 25) + (y ² + 10 y + 25) = 49
(x - 5)² + (y - (- 5) )² = 7²
Centre (5 , - 5)
Radius = 7

Answer 2

group x's and y's and complete squares

(x^2-10x +25) + (y^2+10y +25) +50 = 49+ 25+25
then
(x-5)^2 + (y+5)^2 = 49-50+25+25
so get
(x-5)^2 +(y+5)^2) = 49
or
(x-5)^2 +(y+5)^2= 7^2

center at
(5,-5)
radius is 7