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decide whether or not the equation has a circle as it's graph. if it does, give the center and the radius. if it does describe the graph:x^2+y^2+6x-8y+26=0

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Explanation:

the basic form of a circle is

(x - h)² + (y - k)² = r²

with (h, k) being the center of the circle, "r" being the radius.

when doing the multiplications of the squares :

x² - 2hx + h² + y² - 2ky + k² = r²

x² + y² - 2hx - 2ky + h² + k² - r² = 0

let's compare it to our given equation :

x² + y² + 6x - 8y + 26 = 0

x² matches

y² matches

6x = -2hx

h = -3

-8y = -2ky

k = 4

(-3)² + 4² - r² = 26

9 + 16 - r² = 26

25 - r² = 26

-r² = 1

r² = -1

r = sqrt(-1) = i

so, this is not a circle or any other curve in the world of real coordinates.

User Weez
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