Let x and y be real numbers. If x and y satisfy:
x^2 + y^2 = 4x - 8y + 25 then find the largest value of x and simpify giving your answer in exact form and radicals!
Simplify as
x^2 - 4x + y^2 + 8y = 25 complete the square on x, y
x^2 - 4x +4 + y^2 + 8y + 16 = 25 + 4 + 16
(x - 2)^2 + ( y + 4)^2 = 45
This is a circle centered at ( 2 , -4) with a radius of sqrt (45) = 3sqrt (5)
Largest value of x = 2 + 3sqrt (5)
thank you so much!
+39 
