Download Writing Equations of Circles and Parabolas

Algebra 2
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Writing Equations of Circles and Parabolas
Date________________ Block____
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Use the information provided to write the general conic form equation of each circle.
2
2
2
1) ( x + 13) + y = 9
2
2) ( x − 16) + ( y − 10) = 1
Use the information provided to write the standard form equation of each circle. (complete the square)
3) 28 y + x 2 + y 2 = −349 + 26 x
4) y 2 + 144 − 2 x = 24 y − x 2
5) 18 x + y 2 + x 2 = −14 y − 114
6) 0 = −109 − x 2 + 10 y − 20 x − y 2
Use the information provided to write the standard form equation of each circle.
7) Ends of a diameter: (9, −15) and (1, −3)
8) Ends of a diameter: (16, −9) and (10, −11)
9) Center: (6, −12)
Area: 16π
10) Center: (−6, 14)
Area: 16π
11)
12)
8
y
1
0.5
7
−5
6
−4
−3
−2
−1
1 x
−0.5
5
−1
−1.5
4
−2
3
−2.5
2
−3
−3.5
1
−4
−1
1
2
3
4
5
6
7
−4.5
8 x
−1
−5
13)
1
14)
y
8
0.5
−4
y
−3
−2
−1
−0.5
y
7
1
6
2 x
5
−1
4
−1.5
3
−2
2
−2.5
1
−3
−5 −4 −3 −2 −1
−3.5
−1
−4
−2
−4.5
−3
−5
−4
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1
2
3
4
5
6
7 x
Worksheet by Kuta Software LLC
Use the information provided to write the standard form equation of each parabola.
(
15) Vertex at origin, Focus: 0, −
1
12
)
5
12
( )
16) Vertex at origin, Focus: 0,
Use the information provided to write the vertex form equation of each parabola.
17) Vertex: (6, −1), Directrix: x =
19)
8
23
4
18) Vertex: (−4, −5), Directrix: x = −
20)
y
7
7
y
6
6
5
5
4
4
3
3
2
2
1
1
−2
33
8
−1
1
2
3
4
5
−5
6 x
−4
−3
−2
−1
−1
1
2
3 x
−1
21)
1
22)
y
6
y
5
−6
−5
−4
−3
−2
−1
1 x
4
−1
3
2
−2
1
−3
−4
−3
−2
−1
1
2
3
4
−1
−4
5
6 x
−2
−5
−3
−4
Use the information provided to write the standard form equation of each parabola.
23) f ( x) = −2 x 2 + 20 x − 51
25) −( y + 2) = ( x − 10)
2
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24)
1
( x + 10) = ( y + 1) 2
2
26) −14 x − 61 = −2 y + x 2
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Worksheet by Kuta Software LLC
Answers to Writing Equations of Circles and Parabolas
1) x 2 + y 2 + 26 x + 160 = 0
2
2
7) ( x − 5) + ( y + 9) = 52
2
2
13) ( x + 1) + ( y + 3) = 1
1
2
19) f ( y) = − ( y − 6) + 4
4
25) f ( x) = − x 2 + 20 x − 102
2
2
3) ( x − 13) 2 + ( y + 14) 2 = 16
5) ( x + 9) + ( y + 7) = 16
2
2
2
2
9) ( x − 6) + ( y + 12) = 16
11) ( x − 4) + ( y − 4) = 9
2
15) y = −3 x 2
17) f ( y) = ( y + 1) + 6
2
23) f ( x) = −2 x 2 + 20 x − 51
21) f ( y) = ( y + 3) − 5
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Worksheet by Kuta Software LLC