Decentered Circles Worksheet - Prof. Townsend, 2015
ADVERTISEMENT
1
2
3Decentered Circles – Determine General Form by Pattern Matching
Prof. Townsend
Fall 2015
The general form of a decentered circle is, as given in section 21.3 of Washington,
(x − h)
+ (y − k)
= r
2
2
2
(1)
The problem is to figure out h, k, and r from a problem presented in the form
+ Ay
+ Dx + Ey + F = 0
2
2
(2)
Ax
Using equation 6.4 in Washington we expand then rearrange equation (1).
+ y
− 2hx − 2ky + h
+ k
= r
2
2
2
2
2
(3)
x
The goal is compare equations (2) and (3) to find h, k, and r from pattern matching.
First move the r
2
to the left to get
+ y
− 2hx − 2ky + h
+ k
− r
= 0
2
2
2
2
2
(4)
x
Recall equation (2)
+ Ay
+ Dx + Ey + F = 0
2
2
(2)
Ax
Page 1 of 3
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education