Given a circle with endpoints of a diameter at –10 – 1i and 6 + 11i, answer the questions below. 1. The center of the circle is at + i.
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Answer:
(x+11)
2
+(y−2)
2
=128
Explanation:
(x−h)
2
+(y−k)
2
=r
2
Where C:(h,k)
_________
To find the center, use the midpoint formula
C:(
2
x
1
+x
2
,
2
y
1
+y
2
)
⇒C:(
2
−7+−15
,
2
−2+6
)
⇒C:(−11,2)
__________
To find the diameter, use the distance formula
d=
(x
1
−x
2
)
2
+(y
1
−y
2
)
2
⇒d=
(−7−−15)
2
+(−2−6)
2
⇒d=
8
2
+(−8)
2
⇒d=
128
⇒d=8
2
Thus, radius of the circle will be,
r=
2
8
2
∴r=4
2
Therefore, the equation of the circle is
(x+11)
2
+(y−2)
2
=(4
2
)
2
∴(x+11)
2
+(y−2)
2
=32
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