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Homework Help: Checking: Circle Equations Questions

  1. Feb 3, 2008 #1
    [SOLVED] Checking: Circle Equations Questions

    Last time I got people to check my homework here, I got things marked wrong when they where said to be right. Lets see if it happens again...

    1. The problem statement, all variables and given/known data

    (1) The circle C has centre (3, 4) and passes through the point (8, 8).
    Find an equation for C.

    (2) Find the centre and radius of the circle x² + y² + 4x + 6y – 17 = 0

    (3) A(4, 0) and B(3, 5) are the end points of a diameter of the circle C.
    Find (a) the exact length of AB,
    (b) the coordinates of the midpoint P of AB,
    (c) an equation for the circle C.

    2. Relevant equations

    None

    3. The attempt at a solution

    Right here is my working for (1)

    Since we know the circle centre and a point the circle passes through, I can use pythag to work on the radius right? It seems a little too simple to work, but I can't see anything wrong with it. After drawing a clear diagram;

    (4+8)² + 5² = r²
    r² = 144 + 25
    r² = 169
    r = 13

    Therefore the equation must be (x-3)² + (y-4)² = 13
    Correct?

    Now, my working for (2);

    The equation needs to be factorised, so I have to "complete the square" to get the stuff inside the brackets. This is usually where I go wrong, so check this bit carefully please!

    (x+2)² - 4 + (y+3)² - 9 - 17 = 0

    Rearraged:

    (x+2)² + (y+3)² = 17

    Ah, I have to go now, but I'll post the answers to 3 quickly:

    a) I got 5.09
    b) x = 3.5
    y = 2.2
    and
    c) (x+3.5)² + (y+2.2)² = 5.09

    Sorry about that lack of working out. Thank you for your time if you've read this far!
     
  2. jcsd
  3. Feb 3, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    1) looks fine. I would make 2) to be (x+2)^2+(y+3)^2=30. Is that just a typo? For 3) they ask for the EXACT value of the length of AB, so I would write sqrt(26) rather than the approximation 5.09.
     
  4. Feb 4, 2008 #3
    Thanks! Gotta hand it in later today, so we'll see if I've got them right.
     
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