Unit 5T Name: Date: Integrated Math 4G: HMWK

Unit 5T: Conic Sections Using Technology – Days 1-5 Homework

Day 1 Homework – Introduction to “Conics App” Green Notes (#1-4) “Where is this ever used in real life?” Conics are seen a lot in real life, many times as 3D objects. Their shapes are very “in tune” with nature and natural things. Research things such as “circles in real life”…etc. to find two examples of conics in real life for each of the four conics. 1) Circles 2) Ellipses 3) Hyperbolas 4) Parabolas (#5-12) Label each of the following conics by name based on the equations. 5) 𝑥2

36+ 𝑦2

9= 1 6) (𝑦+2)2

81− (𝑥−1)2

64= 1 7) (𝑥 − 3)2 + (𝑦 + 3)2 = 36

8) 𝑥2

36− (𝑦−2)2

9= 1 9) (𝑥 − 4)2 = 8(𝑦 + 6) 10) (𝑥 − 2)2 + (𝑦 + 1)2 = 49

11) (𝑥−1)2

49+ (𝑦+3)2

81= 1 12) (𝑦 + 3)2 = 16(𝑥 − 7)

(#13-18) Label each of the following conics by name based on the graphs. 13)

14)

15)

16)

17)

18)

Unit 5T

Day 2 Homework – Exploring the Circle Equation Yellow Notes This assignment MUST be completed entirely on graph paper!

(#1-4) For the following equations, find the center and the radius of the circles. 1) (𝑥 − 6)2 + (𝑦 − 3)2 = 36 2) (𝑥 − 7)2 + 𝑦2 = 49 3) (𝑥 + 2)2 + (𝑦 − 3)2 = 4 4) 𝑥2 + (𝑦 + 6)2 = 81 (#5-8) Write the equations of the circles with the given centers and radii. 5) Center is (5, 8) 6) Center is (6, 10) 7) Center is (−7, 8) 8) Center is (0, 1) Radius is 4 Radius is 8 Radius is 9 Radius is 5 (#9-10) Write the equation of the circle in center-radius form by completing the square. Then draw the graph of the circle on an 𝑥-𝑦 plane you create. 9) 𝑥2 + 𝑦2 + 14𝑥 − 12𝑦 + 4 = 0 10) 𝑥2 + 𝑦2 + 2𝑥 − 10𝑦 − 55 = 0 Day 3 Homework – Exploring the Ellipse Equations Pink Notes This assignment MUST be completed entirely on graph paper!

(#1-2) For the following equations, find the center of the ellipse, then find the lengths of the major and minor axes and which axis they are parallel to. 1) (𝑥−1)2

49+ (𝑦−3)2

81= 1 2) (𝑥−8)2

9+ (𝑦+1)2

4= 1

(#3-4) Using the information you found in #1 and #2, sketch the graphs of the following ellipses. 3) (𝑥−1)2

49+ (𝑦−3)2

81= 1 4) (𝑥−8)2

9+ (𝑦+1)2

4= 1

(#5-6) Given the following information about an ellipse, write an equation. 5) Center: (9, 2) 6) Center: (2, −3) Major Axis Length: 10 units Major Axis Length: 18 units Major Axis Parallel to: 𝑦-axis Major Axis Parallel to: 𝑥-axis Minor Axis Length: 4 units Minor Axis Length: 8 units Minor Axis Parallel to: 𝑥-axis Minor Axis Parallel to: 𝑦-axis

Unit 5T Day 4 Homework – Exploring the Hyperbola Equations Blue Notes This assignment MUST be completed entirely on graph paper!

(#1-4) For the following equations, tell whether the hyperbola will open up-down or left-right and label the center. 1) (𝑦+6)2

100 − (𝑥−7)2

49 = 1 2) (𝑥−8)2

16 − (𝑦+12)2

81 = 1 3) (𝑥+7)2

4 − (𝑦+1)2

36 = 1 4) (𝑦−3)2

64 − (𝑥−10)2

9 = 1 (#5-6) For the following graphs, write an equation for the hyperbola. 5)

6)

(#7-10) For the following equations, graph the hyperbola. Be sure to label the vertices and asymptotes. 7) (𝑦−1)2

25− (𝑥−3)2

16= 1 8) (𝑥−2)2

9− (𝑦+2)2

4= 1

9) (𝑦+3)2

36− (𝑥−1)2

9= 1 10) (𝑥+1)2

16− (𝑦+2)2

4= 1

Unit 5T

Day 5 Homework – Exploring the Parabola Equations White Notes This assignment MUST be completed entirely on graph paper!

(#1-4) For the following equations, tell whether the parabola will open up, down, left, or right and state the vertex. 1) (𝑥 − 3)2 = 8(𝑦 − 6) 2) (𝑦 + 5)2 = 2(𝑥 − 1) 3) (𝑦 − 2)2 = 16(𝑥 + 7) 4) (𝑥 + 2)2 = 4(𝑦 + 8) (#5-6) For the following graphs, write an equation for the parabola. 5)

6)

(#7-8) For the following equations, graph the parabola. Be sure to find and label the vertex, focus, directrix, and axis of symmetry. 7) (𝑦 + 2)2 = 12(𝑥 − 1) 8) (𝑥 − 4)2 = 8(𝑦 + 3)

Unit 5T – Day 1 Name: Date: Integrated Math 4G: HMWK Conic Sections Using Technology – Introduction to “Conics App”

*** A TI-84 is NOT required in order to complete this assignment. *** (#1-4) “Where is this ever used in real life?” Conics are seen a lot in real life, many times as 3D objects. Their shapes are very “in tune” with nature and natural things. Research things such as “circles in real life”…ect. to find two examples of conics in real life for each of the four conics. 1) Circles 2) Ellipses 3) Hyperbolas 4) Parabolas (#5-12) Label each of the following conics by name based on the equations. 5) 𝑥2

36+ 𝑦2

9= 1 6) (𝑦+2)2

81− (𝑥−1)2

64= 1

7) (𝑥 − 3)2 + (𝑦 + 3)2 = 36 8) 𝑥2

36− (𝑦−2)2

9= 1

9) (𝑥 − 4)2 = 8(𝑦 + 6) 10) (𝑥 − 2)2 + (𝑦 + 1)2 = 49 11) (𝑥−1)2

49+ (𝑦+3)2

81= 1 12) (𝑦 + 3)2 = 16(𝑥 − 7)

Unit 5T – Day 1 (#13-18) Label each of the following conics by name based on the graphs. 13)

_____________________

14)

_____________________

15)

_____________________

16)

_____________________

17)

_____________________

18)

_____________________

Unit 5T – Day 2 Name: Date: Integrated Math 4G: HMWK Conic Sections Using Technology – Exploring the Circle Equation

*** A TI-84 is NOT required in order to complete this assignment. *** (#1-4) For the following equations, find the center and the radius of the circles. 1) (𝑥 − 6)2 + (𝑦 − 3)2 = 36 2) (𝑥 − 7)2 + 𝑦2 = 49

Center: ( , ) Center: ( , )

Radius: Radius:

3) (𝑥 + 2)2 + (𝑦 − 3)2 = 4 4) 𝑥2 + (𝑦 + 6)2 = 81 Center: ( , )

Center: ( , )

Radius:

Radius:

(#5-8) Write the equations of the circles with the given centers and radii. 5) Center is (5, 8) 6) Center is (6, 10) Radius is 4 Radius is 8 7) Center is (−7, 8) 8) Center is (0, 1) Radius is 9 Radius is 5

Unit 5T – Day 2 (#9-10) Write the equation of the circle in center-radius form by completing the square. Then sketch the graph of the circle. Hint: If you do it right, your circle will fit in the grid given. 9) 𝑥2 + 𝑦2 + 14𝑥 − 12𝑦 + 4 = 0 10) 𝑥2 + 𝑦2 + 2𝑥 − 10𝑦 − 55 = 0

Unit 5T – Day 3 Name: Date: Integrated Math 4G: HMWK Conic Sections Using Technology – Exploring the Ellipse Equations

*** A TI-84 is NOT required in order to complete this assignment. *** (#1-2) For the following equations, find the center of the ellipse, then find the lengths of the major and minor axes and which axis they are parallel to. 1) (𝑥−1)2

49+ (𝑦−3)2

81= 1 2) (𝑥−8)2

9+ (𝑦+1)2

4= 1

Center: ( , ) Center: ( , )

Major Axis Length: Major Axis Length:

Major Axis Parallel to: Major Axis Parallel to:

Minor Axis Length: Minor Axis Length:

Minor Axis Parallel to: Minor Axis Parallel to:

(#3-4) Using the information you found in #1 and #2, sketch the graphs of the following ellipses. 3) (𝑥−1)2

49+ (𝑦−3)2

81= 1 4) (𝑥−8)2

9+ (𝑦+1)2

4= 1

Unit 5T – Day 3 (#5-6) Given the following information about an ellipse, write an equation. 5) Center: (9, 2) 6) Center: (2, −3) Major Axis Length: 10 units Major Axis Length: 18 units

Major Axis Parallel to: 𝑦-axis Major Axis Parallel to: 𝑥-axis Minor Axis Length: 4 units Minor Axis Length: 8 units

Minor Axis Parallel to: 𝑥-axis Minor Axis Parallel to: 𝑦-axis Together Problems: We did not do any examples in the notes, so we will do some here so that you can get a starting point.

Ex 1) (𝑥+4)2

16+ (𝑦−2)2

25= 1 Sketch the graph:

Center: ( , )

Major Axis Length:

Major Axis Parallel to:

Minor Axis Length:

Minor Axis Parallel to:

Ex 2) Center: (−5, 7) Minor Axis Length: 6 units Major Axis Length: 12 units Minor Axis Parallel to: 𝑦-axis

Major Axis Parallel to: 𝑥-axis

Unit 5T – Day 4 Name: Date: Integrated Math 4G: HMWK Conic Sections Using Technology – Exploring the Hyperbola Equations

*** A TI-84 is NOT required in order to complete this assignment. *** (#1-4) For the following equations, tell whether the hyperbola will open up-down or left-right and label the center.

1) (𝑦 + 6)2

100 −(𝑥 − 7)2

49 = 1 2) (𝑥 − 8)2

16 −(𝑦 + 12)2

81 = 1

Opens: Opens:

Center: ( , ) Center: ( , )

3) (𝑥 + 7)2

4 −(𝑦 + 1)2

36 = 1 4) (𝑦 − 3)2

64 −(𝑥 − 10)2

9 = 1 Opens:

Opens:

Center: ( , ) Center: ( , )

(#5-6) For the following graphs, write an equation for the hyperbola. 5)

6)

Unit 5T – Day 4 (#7-10) For the following equations, graph the hyperbola. Be sure to label the vertices and asymptotes. 7) (𝑦−1)2

25− (𝑥−3)2

16= 1 8) (𝑥−2)2

9− (𝑦+2)2

4= 1

9) (𝑦+3)2

36− (𝑥−1)2

9= 1 10) (𝑥+1)2

16− (𝑦+2)2

4= 1

Unit 5T – Day 5 Name: Date: Integrated Math 4G: HMWK Conic Sections Using Technology – Exploring the Parabola Equations (#1-4) For the following equations, tell whether the parabola will open up, down, left, or right and state the vertex. 1) (𝑥 − 3)2 = 8(𝑦 − 6) 2) (𝑦 + 5)2 = 2(𝑥 − 1)

Opens: Opens:

Vertex: ( , ) Vertex: ( , )

3) (𝑦 − 2)2 = 16(𝑥 + 7) 4) (𝑥 + 2)2 = 4(𝑦 + 8) Opens:

Opens:

Vertex: ( , ) Vertex: ( , )

(#5-6) For the following graphs, write an equation for the parabola. 5)

6)

Unit 5T – Day 5 (#7-8) For the following equations, graph the parabola. Be sure to label the vertex, focus, directrix, and axis of symmetry. 7) (𝑦 + 2)2 = 12(𝑥 − 1) 8) (𝑥 − 4)2 = 8(𝑦 + 3) ℎ = _____ 𝑘 = _____ 𝑝 = _____ ℎ = _____ 𝑘 = _____ 𝑝 = _____

Vertex: Focus: Directrix:

Vertex: Focus: Directrix: