# Math Check

posted by Susie

Hi! Can someone check my answer for this question? Thanks!

Question: List the following circles in order based of their radius. List them from smallest to largest.
A.) x^2+y^2-6x+8y-9=0
B.) (x-3)^2=9-(y+4)^2
C.) (y+4)^2=3-(x-3)^2
D.) (x-3)^2+(y+4)^2=1

d,b,c,a

1. Reiny

The only one we actually have to work with is A
let's complete the square:
x^2+y^2-6x+8y-9=0
x^2 - 6x + ... + y^2 + 8y + ... = 9
x^2 - 6x + 9 + y^2 + 8y + 16 = 9+9+16
(x-3)^2 + (y+4)^2 = 34, so its radius is √34

my order from smallest to largest is
D, C, B, A

The radius of B is √9 = 3
the radius of C = √3 which is < 3

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