5
12√15
12√85
√85
Correct answer is C
The equation of a circle is given as (x−a)2+(y−b)2=r2.
Expanding, we have: x2−2ax+a2+y2−2by+b2=r2
x2+y2−2ax−2by+a2+b2=r2
Comparing with the equation, x2+y2−8x+9y=−15, we have
2a=8;2b=−9;r2−a2−b2=−15
a=4;b=−92
∴
= -15 + 16 + \frac{81}{4} = \frac{85}{4}
r = \sqrt{\frac{85}{4} = \frac{1}{2}\sqrt{85}
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