Equations of Circles

Kuta Software - Infinite Algebra 2

Name___________________________________

Writing Equations of Circles

Date________________ Period____

Use the information provided to write the standard form equation of each circle.
1) 8 x + x 2 − 2 y = 64 − y 2

2) 137 + 6 y = − y 2 − x 2 − 24 x

3) x 2 + y 2 + 14 x − 12 y + 4 = 0

4) y 2 + 2 x + x 2 = 24 y − 120

5) x 2 + 2 x + y 2 = 55 + 10 y

6) 8 x + 32 y + y 2 = −263 − x 2

7) Center: (−11, −8)
Radius: 4

8) Center: (−6, −15)
Radius: 5

9) ( x − 16) 2 + ( y − 6) 2 = 1
Translated 4 left, 2 up

10) ( x + 5) 2 + ( y + 7) 2 = 36
Translated 5 left, 4 down

11)

12) y y

7

1

6
−1

1

2

3

4

5

6 x

5
−1
4
−2
3
−3
2
−4

1

−5
−4

−3

−2

−1

1

2

3

4 x

−1

©v i2d0L1d1y 3Kvudtuaa aSJoOfttgwga9rweG LLULbC9.f u kAqlalu PrIicgChvtjsd srhews3ecrZvueCd2.U c xMxaMdFex Dwjidt8hL PIwnhfnijnXiztfeL EAQl2goesbvrfaf a2r.p

-1-

Worksheet by Kuta Software LLC

13) Ends of a diameter: (−17, −9) and (−19, −9)

14) Ends of a diameter: (−3, 11) and (3, −13)

15) Center: (−15, 3 7 )
Area: 2π

16) Center: (−11, −14)
Area: 16π

17) Center: (−5, 12)
Circumference: 8π

18) Center: (15, 14)
Circumference: 2π 15

19) Center: (2, −5)
Point on Circle: (−7, −1)

20) Center: (14, 17)
Point on Circle: (15, 17)

21) Center: (−15, 9)
Tangent to x = −17

22) Center: (−2, 12)
Tangent to x = −5

23) Center lies on the x-axis
Tangent to x = 7 and x = −13

24) Center lies in the fourth quadrant
Tangent to x = 7, y = −4, and x = 17

25) Three points on the circle:
(−18, −5), (−7, −16), and (4, −5)

26) Three points on the circle:
(−7, 6), (9, 6), and (−4, 13)

27) x 2 + y 2 + 14 x + 12 y + 76 = 0
Translated 2 right, 4 down

28) x 2 + y 2 − 10 x + 20 y + 61 = 0
Translated 1 left, 2 down

29) x 2 + y 2 + 14 x − 8 y + 29 = 0
Translated 3 right, 4 down

30) 4 y + y 2 = −28 x − x 2 − 191
Translated 4 right

©C Q2B0Y1T1K XKFumtDai tSQoifFtUwQadrxe7 ELMLTCd.p P eAMl4lo hrLiagGhwtYsA Urzeus0eyrjvteKdg.t k NMsaOdIeo iwci5tzh1 IIvnBfYiPnJigtEeD xA0lTgZelb1rxay