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(x-a)^2 + (y-b)^2 = r^2 is the equation of a circle with rad

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by Max@Math Revolution » Thu Feb 28, 2019 6:16 am

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B

C

D

E

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(x-a)^2 + (y-b)^2 = r^2 is the equation of a circle with radius r and center (a,b). What is the radius of the circle with equation x^2 + y^2 - 10x + 4y = 20?

A. 4
B. 5
C. 6
D. 7
E. 8
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by Max@Math Revolution » Sun Mar 03, 2019 5:16 pm
=>

x^2 + y^2 - 10x + 4y = 20
=> x^2 - 10x + y^2 + 4y = 20
=> x^2 - 10x + 25 + y^2 + 4y + 4 = 20 + 25 + 4
=> (x-5)^2 + (y+2)^2 = 49
=> (x-5)^2 + (y+2)^2 = 7^2

Thus the circle has center (5,-2) and radius 7.

Therefore, the answer is D.
Answer: D
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