1.

x^{2} + y^{2} − 6x + 8y + 21 = 0

2.

x^{2} + y^{2} − 2x − 2y = 14

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

1. rearrange the equation and complete the square.

X^2-6x+9 +y^2+8y+16=-21+9+16

x^2-6x+y^2+8y+16=4

factor the left

(x-3)^2+(y-4)^2=4 the center is (3,4) and the radius is sqrt4=2

2. X^2-2x+1+y^2-2y+1=14+1+1

X^2-2x+1+y^2-2y+1=16

(x-1)^2+(y-1)^2=16

the center is (1,1) and the radius is sqrt 16 which is 4

I hope this is helpful. Please best this answer. Thanks!

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