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19 May, 18:13

Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius? A. (-7, - 1), 36 units B. (7, 1), 36 units C. (7, 1), 6 units D. (-7, - 1), 6 units

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  1. 19 May, 21:14
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    The correct answer is D.

    Step-by-step explanation:

    Given:

    General equation of second degree

    x² + y² + 14 x + 2 y + 14 = 0

    We must transform given equation to the canonical form from which we will read requested data.

    The canonical form of the circle equation is:

    (x - p) ² + (y - q) ² = r²

    Where p and q are the coordinates of the center of the circle and r are radius. (p, q) = (x, y)

    x² + 2 · x ·7 + 7² - 7² + y² + 2 · y · 1 + 1 - 1 + 14 = (x+7) ² + (y+1) - 49 - 1 + 14 = 0

    (x + 7) ² + (y + 1) ² = 36

    We see that p = - 7, q = - 1 and r = 6

    God with you!
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