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15 October, 00:16

Determine the center and radius of the circle described by the question.

(X+2)

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Answers (1)
  1. 15 October, 03:07
    0
    The question is incomplete, I will however explain, with an illustration, how to determine the center and radius of a circle.

    Step-by-step explanation:

    The standard equation of a circle is given as:

    (x - a) ² + (y - b) ² = r² ... (1)

    Where (a, b) is the center of the circle, and r is the radius.

    An expression can be given for us to find the center and the radius of the circle.

    Suppose we were given the expression:

    x² + y² - 10x + 4y - 7 = 0 ... (2)

    To find the center and the radius, it is left for us to rewrite (2) in the form of (1).

    Rearranging (2), we have

    (x² - 10x) + (y² + 4y) = 7

    Completing the squares of each bracket

    (x² - 10x + 25 - 25) + (y² + 4y + 4 - 4) = 7

    (x² - 10x + 25) + (y² + 4y + 4) - 25 - 4 = 7

    (x² - 10x + 25) + (y² + 4y + 4) - 29 = 7

    (x - 5) ² + (y + 2) ² = 7 + 29

    (x - 5) ² + (y + 2) ² = 36

    Or

    (x - 5) ² + (y + 2) ² = 6² ... (3)

    Comparing (3) with one, we see that

    a = 5, b = - 2, and r = 6

    Therefore it is a circle centered at (5, - 2) with a 6 unit radius.
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