#1**+8 **#### x² + y² = 10x + 5y -25 subtract 10x, 5y from both sides, so we have

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"

CPhill
Dec 16, 2014

#1**+8 **

Best Answer#### x² + y² = 10x + 5y -25 subtract 10x, 5y from both sides, so we have

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"

CPhill
Dec 16, 2014