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14 June, 13:14

Find the center and the radius of the circle with the equation:

x^2 + 6x + y^2 + 4y + 12 = 0

a.

center: (3, 2)

radius: 1

c.

center: (6, 4)

radius: 12

b.

center: (-3, - 2)

radius: 1

d.

center: (-6, - 4)

radius: 12

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Answers (1)
  1. 14 June, 13:32
    0
    Center is (-3, - 2) and radius is 1

    Step-by-step explanation:

    Step 1: Given equation of the circle is x² + 6x + y² + 4y + 12 = 0. Standard form is x² + y² + 2gx + 2fy + c = 0. Center is (-g, - f) and radius is √g² + f² - c. Find g, f and c.

    By comparing the 2 equations,

    ⇒ 2gx = 6x

    ⇒ 2g = 6

    ∴ g = 6/2 = 3

    ⇒ 2fy = 4y

    ⇒ 2f = 4

    ∴ f = 4/2 = 2

    ⇒ c = 12

    Step 2: Find center and radius.

    Center = (-g, - f) = (-3, - 2)

    Radius = √g² + f² - c

    = √3² + 2² - 12 = √9 + 4 - 12

    = 1
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