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10 July, 10:29

Which coordinate pair identifies the center of the circle represented by 4x2 + 4y2 - 16x - 24y + 36 = 0.

A) (2, 3)

B) (3, 2)

C) (0, 0)

D) (-3, 2)

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Answers (1)
  1. 10 July, 10:42
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    Answer

    Find out the which coordinate pair identifies the center of the circle represented by 4x² + 4y² - 16x - 24y + 36 = 0.

    To prove

    The general equation of the circle is

    (x - h) ² + (y - k) ² = r²

    Where h, k are the centre and r is the radius.

    4x² + 4y² - 16x - 24y + 36 = 0

    Divided both side by 4.

    x² + y² - 4x - 6y + 9 = 0

    Add and subtract 4 and 9

    x² + y² - 4x - 6y + 4 - 4 + 9 - 9 + 9 = 0

    x² + y² - 4x - 6y + 4 - 4 + 9 - 9 + 9 = 0

    x² + 4 - 2 * 2 * x + y² + 9 - 2 * 3 * y = 9 + 4 - 9

    using the formula (a + b) ² = a² + b² + 2ab

    (x - 2) ² + (y - 3) ² = 2²

    Compare this with the general equation of circle.

    Thus

    h = 2, k = 3

    Option A is correct.
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