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The equation of a circle is \(x^{2} + y^{2} - 8x + 9y + 15 =...

The equation of a circle is x2+y28x+9y+15=0. Find its radius.

A.

5

B.

1215

C.

1285

D.

85

Correct answer is C

The equation of a circle is given as (xa)2+(yb)2=r2.

Expanding, we have: x22ax+a2+y22by+b2=r2

x2+y22ax2by+a2+b2=r2

Comparing with the equation, x2+y28x+9y=15, we have

2a=8;2b=9;r2a2b2=15

a=4;b=92

= -15 + 16 + \frac{81}{4} = \frac{85}{4}

r = \sqrt{\frac{85}{4} = \frac{1}{2}\sqrt{85}