Deriving The Equation Of A Circle Date Page 3
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1
2
3Practice – Unit 9 (cont.)
C)
Given Center and Point on Circle:
Find the radius if the center is at (0, -5) and one point on the circle is (2, 3). (
)
Use the distance formula!
(
) (
)
−
2
+
−
2
x
x
y
y
2
1
2
1
(
)
(
)
( )
2
−
2
+
− −
2 0
3
5
( ) ( )
2
+
2
=
+
=
=
2
8
4 64
68
2 17
Radius =
2 17
D) Given endpoints of the diameter:
Write the equation of a circle whose diameter has endpoints (4, -1) and (-6, 7).
(
)
Use the distance formula, then divide by 2
(
) (
)
−
2
+
−
2
x
x
y
y
2
1
2
1
(
)
(
)
( )
( )
2
2
− −
+ − −
4
6
1
7
( ) ( )
2
+ − =
2
+ =
=
10
8
100 64
164
2 41
Radius =
(
)
after you divide by 2!
41
Determining whether a point is ON / IN / OUTSIDE the circle:
In order to determine the position of a point in relation to a given circle, you must compare the
distance from the center to the point.
a) For points ON the circle:
the distance _____ the radius
b) For points IN the circle:
the distance _____ the radius
c) For points OUTSIDE the circle:
the distance _____ the radius
C
B
D
A
ON / IN / OUTSIDE because AB ____ radius length. (chose <, >, or =)
, B is
In
A
ON / IN / OUTSIDE because AC ____ radius length. (chose <, >, or =)
, C is
In
A
ON / IN / OUTSIDE because AD ____ radius length. (chose <, >, or =)
, D is
In
A
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