1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Set of points specified by x^2 + y^2 <= 4x + 4y

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    What set of points is specified by the inequality x^2 + y^2 ≤ 4x + 4y

    2. Relevant equations

    x^2 + y^2 = r^2 is the formula for a circle with its center at the origin

    3. The attempt at a solution

    x^2 - 4x + y^2 - 4y ≤ 0 ??????

    The book gives the solution, if you want me to post it i can. But i didn't understand how they got it
    Last edited: Dec 16, 2011
  2. jcsd
  3. Dec 16, 2011 #2


    Staff: Mentor

    This is actually an inequality, not an equation.
    Complete the square in the x terms and in the y terms. The < part of the inequality represents all of the points inside a circle. The = part represents all the points on the circle.
  4. Dec 16, 2011 #3
    ninja edited :wink:

    are we completing the square to get the inequality in the familiar (x-a)^2 + (y-a)^2 = R^2 form that represents a circle? So it would be (x-2)^2 + (y-2)^2 ≤ 8

    So apparently that means the same thing as (x-0)^2 + (y-0)^2 ≤ 4x + 4y, even though (x-0)^2 + (y-0)^2 would indicate that the circle is at the origin whereas (x-2)^2 + (y-2)^2 is for a circle with the center at (2,2).

    Could someone help me understand why setting (x-0)^2 + (y-0)^2 less than or equal to "4x + 4y" rather than a number can make the circle centered at (2,2) instead of the origin as (x-0) and (y-0) led me to believe?
  5. Dec 16, 2011 #4


    Staff: Mentor

    Yes. This inequality can be separated into two statements:
    (x-2)^2 + (y-2)^2 < 8
    (x-2)^2 + (y-2)^2 = 8
    The inequality represents all the point inside the circle.
    The equation represent all the points on the circle.

    Together, the ≤ represents all the points on the circle or inside it.
    Yes, but this form is not helpful at all.
  6. Dec 16, 2011 #5

    Thanks Mark44!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook