Algebra

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State the center and the radius of the circle represented by the equation

(x + 1)^2 + (y – 5)^2 = 64

  • Algebra -

    If you tried to copy and paste, that does not work here.

  • Algebra -

    State the center and the radius of the circle represented by the equation

    (x + 1^2 + (y – 5)^2 = 64

  • Algebra -

    I think the radius is 8 but am stuck on what the center represents here.

  • Algebra -

    You mean (x+1)^2
    Now this is the same both sides of x = -1
    Like for x = -2 and for x = 0
    in both cases (x+1)^2 = +1
    In other words, x = -1 is an axis of symmetry and the circle center must lie on x = -1
    Same thing for y = 5
    so the center is at (-1,+5)
    NOW
    in general:
    (x-h)^2 + (y-k)^2 = r^2
    is circle with radius r
    and center at (h,k)

  • Algebra -

    I did get (-1,5) as well, but why is it -1 rather than 1? I was just wondering.

  • Algebra -

    (x-h) = (x+1)
    so
    -h = +1
    h = -1

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