What is the radius of the circle given by the equation below?

x 2 + 18 x + y 2 + 18 y = − 146 ( x 2 + 18 x + 81 ) + ( y 2 + 18 y + 81 ) − 81 − 81 = − 146 ( x + 9 ) 2 + ( y + 9 ) 2 = − 146 + 81 + 81 ( x + 9 ) 2 + ( y + 9 ) 2 = − 146 + 162 ( x + 9 ) 2 + ( y + 9 ) 2 = 16
T hi s i s in t h e g e n er a l c i rc l e f or m : ( x − h ) 2 + ( y − k ) 2 = r 2 , so : r 2 = 16 r = 16 ​ r = 4 A n s w er : C .4

Answered by Lilith | 2024-06-10

To find the radius of the circle, rearrange the equation into standard form ( x − h ) 2 + ( y − k ) 2 = r 2 where r is the radius. By completing the square, you can determine the value of r directly. For the equation x 2 + y 2 − 10 x + 8 y + 24 = 0 , the radius is approximately 4.12.
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Answered by Lilith | 2024-12-26