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Write x^2+y^2-6x+8y+9=0 in the standard form of a circle

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Write x^2+y^2-6x+8y+9=0 in the standard form of a circle

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The equation of a circle with radius r and center (h, k) in standard form is (x - h)^2 + (y - k)^2 = r^2.

The equation given is x^2 + y^2 - 6x + 8y + 9 = 0

x^2 + y^2 - 6x + 8y + 9 = 0

=> x^2 - 6x + y^2 + 8y + 9 = 0

=> x^2 - 6x + 9 + y^2 + 8y + 16 = 9 + 16 - 9

=> (x - 3)^2 + (y + 4)^2 = 4^2

This is the equation of a circle with center (3, -4) and radius 4

The standard form of x^2 + y^2 - 6x + 8y + 9 = 0 is (x - 3)^2 + (y + 4)^2 = 4^2

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