Find the largest value of x for which
x^2 + y^2 = 4x + 5y
has a solution, if x and y are real.
Notice that x2+y2=4x+5y is very similar to the equation of a circle.
We have x2−4x+y2−5y=0.
Now, completing the square for both x and y, we get
(x−2)2+(y−5/2)2=25/4+16
This is the official equation of a circle.
It has the center at (2,5/2) and a radius of √89/4
The largest value of x is basically the x value of the center added to the radius.
Thus, we have 2+√892=4+√892
So our final answer is 4+√892
Thanks! :)
Notice that x2+y2=4x+5y is very similar to the equation of a circle.
We have x2−4x+y2−5y=0.
Now, completing the square for both x and y, we get
(x−2)2+(y−5/2)2=25/4+16
This is the official equation of a circle.
It has the center at (2,5/2) and a radius of √89/4
The largest value of x is basically the x value of the center added to the radius.
Thus, we have 2+√892=4+√892
So our final answer is 4+√892
Thanks! :)