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Circles Practice Classwork, Assignments of Geometry

Circles Practice Classwork Is discussed

Typology: Assignments

2016/2017

Uploaded on 04/29/2024

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Accel Geo B/Alg II
Name: _____________________________
Circles Practice Classwork
Period: ______ Date: _______________
Section 1
Use the information provided to write the equation of each circle in standard and general form.
1) Center: (-13, 0) 2) Center: (17, 16)
Radius: 4 Point on the circle: (-2, 11)
3) Center: (7, -8) 4) Endpoints of a Diameter of a Circle:
Tangent line on the y-axis (-10, -2) and (-8, 14)
Section 2
Identify the center and radius of each circle, then sketch the graph.
5) (x + 3
2)2+ (y 4)2= 5 6) (x + 1)2+ (y 3)2= 9 7) 𝑥2+ (y + 1)2=20
Section 3
Use the information provided to write the standard form equation of each circle:
8) 𝑥2+ 𝑦 2 8𝑥 + 8𝑦 32 = 0 9) 𝑥2+ 𝑦 224𝑥 + 120 = 0
10) 𝑥2+ 𝑦2+ 4𝑥 + 14𝑦 47 = 0 11) 𝑥2+ 𝑦211𝑦 + 3 = 0
Section 4
Determine if the following points are on, inside, or outside the circle (x + 2)2+ (y 4)2=400
12) Point: (-2, 24) 13) Point: (0, 26) 14) Point: (14, -7)
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Accel Geo B/Alg II

Name: _____________________________

Circles Practice Classwork Period: ______^ Date: _______________

Section 1 Use the information provided to write the equation of each circle in standard and general form.

  1. Center: (-13, 0 ) 2) Center: (17, 16) Radius: 4 Point on the circle: (-2, 11)
  2. Center: (7, - 8 ) 4) Endpoints of a Diameter of a Circle: Tangent line on the y-axis (-10, - 2 ) and (-8, 14) Section 2 Identify the center and radius of each circle, then sketch the graph.
  3. (x + 3 2 ) (^2) + (y − 4 ) (^2) = 5 6) (x + 1 ) (^2) + (y − 3 ) (^2) = 9 7) 𝑥 (^2) + (y + 1 ) (^2) = 20 Section 3 Use the information provided to write the standard form equation of each circle: 8 ) 𝑥^2 + 𝑦^2 − 8 𝑥 + 8 𝑦 − 32 = 0 9 ) 𝑥^2 + 𝑦^2 − 24 𝑥 + 120 = 0 10 ) 𝑥^2 + 𝑦^2 + 4 𝑥 + 14 𝑦 − 47 = 0 11 ) 𝑥^2 + 𝑦^2 − 11 𝑦 + 3 = 0 Section 4 Determine if the following points are on, inside, or outside the circle (x + 2 )^2 + (y − 4 )^2 = 400
  4. Point: (-2, 24) 13) Point: (0, 26) 14) Point: (14, - 7 )

Determine if the following points are on, inside, or outside the circle x^2 + y^2 + 2x − 10y − 599 = 0 15 ) Point: (- 6 , 2 9 ) 16 ) Point: (23, - 2) 17 ) Point: (-25.5, 5.5) Section 5

  1. Does the point (-3, 45) lie on the circle centered at (-6, - 5), and containing the point (15, - 35)?
  2. Does the point (-4, - 1) lie on the circle centered at (3, 5) and containing the point (7, 2)?
  3. Write the following equations in standard form and identify the center and radius. a) 8 𝑥 + 𝑥^2 − 2 𝑦 = 64 − 𝑦^2 b) 137 + 6 𝑦 = −𝑦^2 − 𝑥^2 − 24 𝑥
  4. Graph the following equations. a) 𝑥^2 + 𝑦^2 + 6 𝑥 − 8 𝑦 + 9 = 0 b) − 1 − 4 𝑦 + 4 𝑥 = −𝑦^2 − 𝑥^2 Section 6
  5. For each problem below, write the equation of the line tangent to the given circle at the given point. a) 𝑥^2 + 𝑦^2 = 16 , (4, 0) b) (𝑥 − 5 )^2 + (𝑦 + 1 )^2 = 25 , (2, - 5) c) 𝑥^2 + 𝑦^2 − 4 𝑥 − 8 𝑦 − 269 = 0 , (2, 21 ) d) 𝑥^2 − 2 𝑥 = 2 𝑦 − 𝑦^2 + 23 , ( 5 , - 2 )