+864 Let x and y be real numbers. If x and y satisfy
x^2 + y^2 = 4x + 2y
then find the largest possible value of x. Give your answer in exact form using radicals, simplified as far as possible.
+1950 First off, let's move all the terms to one side of the equation before combining like terms!
x2−4x+y2−2y=0
Completing the square for x and y, we get
x2−4x+4+y2−2y+1=4+1(x−2)2+(y−1)2=5
Wait! This is the equation for a circle.
Using the equations for circles, this circle has a radius of √5 and center (2, 1).
The largest value of x would be x=2+√5.
The reason for this is because the largest value of x would just be the radius plus the x value of the center!
Thanks! :)
+1950 First off, let's move all the terms to one side of the equation before combining like terms!
x2−4x+y2−2y=0
Completing the square for x and y, we get
x2−4x+4+y2−2y+1=4+1(x−2)2+(y−1)2=5
Wait! This is the equation for a circle.
Using the equations for circles, this circle has a radius of √5 and center (2, 1).
The largest value of x would be x=2+√5.
The reason for this is because the largest value of x would just be the radius plus the x value of the center!
Thanks! :)
