Show that the equation represents a circle by rewriting it i

Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle. X^2 + y^2 - 6x + 4y + 12 = 0 standard form Center (x, y) = () radius Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle. X^2 + y^2 + y = 0 standard form Center (x, y) = () radius

Solution

9)
The given equation is:
x^2 + y^2 - 6x + 4y + 12 = 0
rearranging,
x^2 -6x + 9 + y^2 + 4y + 4 -1 = 0
(x^2 -6x + 9) + (y^2 + 4y + 4) -1 = 0
(x^2 -6x + 9) + (y^2 + 4y + 4) = 1
(x-3)^2 + (y+2)^2 = 1

standard form:
(x-3)^2 + (y+2)^2 = 1

centre
(3,-2)

radius:
1

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