Homework LogTues

12/1

Lesson 4 – 5

Learning Objective: To graph translation of ellipses and hyperbolas

Hw: #406 Pg. 247 #1, 3, 9, 13, 19, 25 - 35 odd (find foci #1,3,9)

12/1/15 Lesson 4 – 5 Translation of Ellipses &

HyperbolasAdvanced Math/Trig

Learning Objective To graph translation of ellipses

To graph translation of hyperbolas

To write equations of translated ellipses & hyperbolas

Standard Equation of Ellipse

Center (h, k) a = major b = minor

Ellipse “a” is the bigger #Foci is always on MAJOR axis

If x is major axis F()If y is major axis F(h, )

Graph 1. Major Axis: yMinor Axis: xa = 4 b = 3 c =

C (1, 2)V ()V (1, –2)CV (–2, CV (4, 2)F (1, )

(1, 2) (4, 2)(–2, 2)

(1, 6)

(1, –2)

Graph2. __+ ___ __+ ___

4 41 4Major Axis: xMinor Axis: ya = 4 b = 2 c =

Graph 2.

C (–2, 1)V (–6, 1)V (2, 1)CV (–2, 3CV (–2, –1)F (–2, 1)

(–2, 1) (2, 1)(–6, 1)

(–2, 3)

(–2, –1)

Major Axis: xMinor Axis: ya = 4 b = 2c =

Write a standard equation

3. Write a standard equation of an ellipse with C(–3, 2) and V(–3, –3) and

V(–3, 7) and endpoints of minor axis at (–5, 2) & (–1, 2)

Major: y Minor: xa = 5 b = 2 2

5

Write a standard equation

4. Write a standard equation of an ellipse with C(0, 0), x – int:

y – int:

Standard Equation of Hyperbola

Center (h, k) *“a” always “positive”*Dot a box with & from the center to find asymptotesFoci is always on the way it “opens”

If opens “x” F()If opens “y” F(h, )

Graph 5. Opens: xa = 3 b = 2 c =

C (–1, 1)V (–) V (2, 1)F (– )

(–1, 1) (2, 1)(–4, 1)

(–1, 3)

(–1, –1)

Graph6. __+ __ _

1 14 –16Opens: y

a = 4 b = 2 c =

Graph 6.

C (2, –1)V (2, –5)V (2, 3)F (2, –1)

Opens: ya = 4 b = 2c =

(2, –1)

(2, 3)

(2, –5)

(4, –1)(0, –1)

Rewrite in Standard Form. Identify as Ellipse, Circle, or

Hyperbola7. __+ _ _

4 361 –1HyperbolaOpens: ya = 3 b = 1Center (2, 1)

Rewrite in Standard Form. Identify as Ellipse, Circle, or

Hyperbola8. __+ __ _

9 814 64EllipseMajor: xa = 4 b = 3Center (3, –2)

Rewrite in Standard Form. Identify as Ellipse, Circle, or

Hyperbola8. __+ __ 16

9 916 16

CircleCenter (–3, 4)Radius =

Ticket Out the Door Write in standard form What shape is it? Graph it. Find vertices and foci

Homework#406 Pg. 247 #1, 3, 9, 13, 19, 25 -

35 odd (find foci #1,3,9)