Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

1. x^{2} + y^{2} − 8x + 8y + 16 = 0

2. x^{2} + y^{2} + 10y + 18 = 0

3. x^{2} + y^{2} + x = 0

x^2 - 8x + y^2 +8y = -16

(x -4)^2 + (y+4)^2 = -16 + 16 +16 = 16

So, the center is (4,-4) with radius 4

x^2 + y^2 + 10y = -18

x^2 + (y+5)^2 = -18 + 25 = 7

So, the center is (0,-5) with radius sqrt(7)

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