T h e e q u a t i o n o f a c i rc l e w i t h ce n t re ( a , b ) an d r a d i u s " r " i s : ( x − a ) 2 + ( y − b ) 2 = r 2
( 12 , − 14 ) , ( 2 , 4 ) S in ce t h e ce n t er o f t h e c i rc l e i s t h e mi d p o in t o f t h e l in e se g m e n t co nn ec t in g tw o e n d p o in t s o f a d iam e t er M i d p o in t F or m u l a ( a , b ) = ( 2 x 1 + x 2 , 2 y 1 + y 2 ) = ( 2 12 + 2 , 2 − 14 + 4 ) = ( 2 14 , 2 − 10 ) = ( 7 , − 5 )
T h e r a d i u s i s t h e d i s t an ce f ro m t h e ce n t er t o so m e p o in t o n t h e c i rc l e . T h e d i s t an ce f ro m ( 7 , − 5 ) t o ( 12 , − 14 ) i s : r = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 r = ( 12 − 7 ) 2 + ( − 14 + 5 ) 2 = 5 2 + ( − 9 ) 2 = 25 + 81 = 106 ( x − 7 ) 2 + ( y − ( − 5 ) ) 2 = ( 106 ) 2 ( x − 7 ) 2 + ( y + 5 ) 2 = 106
To find the equation of a circle with endpoints (12, -14) and (2, 4) as its diameter, we first calculate the midpoint to find the center, which is (7, -5). Next, we use the distance formula to find the radius, which is 106 . Finally, the equation can be expressed as ( x − 7 ) 2 + ( y + 5 ) 2 = 106 .
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jawabannya ya kak, ambil gambarnya saja ya