x^2 - 10x + y^2 - 5y = -25 complete the square on x and y..... so we have
x^2 - 10x + 25 + y^2 - 5y + 25/4 = -25 +25 + 25/4 factor and simplify
(x - 5)^2 + ( y - 5/2)^2 = 25/4
So, this is a circle whose center is ( 5, 5/2) and whose radius is 5/2
Now if we wanted this in terms of y.....first subtract (x - 5)^2 from both sides
( y - 5/2)^2 = 25/4 - (x - 5)^2 take the positive and negative square root of both sides
y -5/2 = ±√[25/4 - (x - 5)^2] add 5/2 to both sides
y = ±√[25/4 - (x - 5)^2] + 5/2
And that's everything in terms of 'y"
x^2 - 10x + y^2 - 5y = -25 complete the square on x and y..... so we have
x^2 - 10x + 25 + y^2 - 5y + 25/4 = -25 +25 + 25/4 factor and simplify
(x - 5)^2 + ( y - 5/2)^2 = 25/4
So, this is a circle whose center is ( 5, 5/2) and whose radius is 5/2
Now if we wanted this in terms of y.....first subtract (x - 5)^2 from both sides
( y - 5/2)^2 = 25/4 - (x - 5)^2 take the positive and negative square root of both sides
y -5/2 = ±√[25/4 - (x - 5)^2] add 5/2 to both sides
y = ±√[25/4 - (x - 5)^2] + 5/2
And that's everything in terms of 'y"