Find the largest value of x for which
x^2 + y^2 = 4x + 5y
has a solution, if x and y are real.
This is the equation of a circle ....look for the right side of the circle ....
x^2 - 4x + 4 + y^2 - 5y + 6.25 = 10.25
(x-2)^2 + ( y- 2.5)^2 = 10.25 This is the cirlce....with center at 2,2.5 and radius sqrt (10.25)
the largest 'x' value will be 2 + sqrt (10.25) = 5.2015 units