Warm-Up 4/24

Parabola

𝑥2+ y2=15𝑥2

12+ 𝑦

2

3=1

Circle

Ellipse

Hyperbola

Rigor:You will learn to identify and write

equations of translated conic sections.

Relevance:You will be able to solve real world

problems using the equation of translated conic section.

10-6 Translating Conic Sections

What is the standard-form equation of an ellipse with vertices (2, 3) and (22, 3), and one focus at (6, 3)? Sketch the ellipse.Center is the midpoint between the vertices.

Center =

a = 12 – 2 = 10

c = 12 – 6 = 6

a is the distance from the center to a vertex.

c is the distance from the center to a focus.

Use c² = a² – b² to find b.

36 = 100 – b²

– 64 = – b²

64 = b²

Co-vertices (12, – 5) & (12, 11)

±8 = b

(𝑥−12 )2

100+

( 𝑦− 3 )2

64=1

(𝑥−h )2

a ²+

(𝑦−𝑘 )2

b ²  =1 •• •

•

•

• •

a² = 100

c² = 36

¿ ( 242

,62 )

Difference in x-coordinates: Horizontal

What are the center, vertices, foci, and asymptotes of the hyperbola with equationSketch the hyperbola.

Center (2, – 2)

a² = 36 a = ± 6vertices (– 4, – 2) & (8, – 2)

Use c² = a² + b² to find c.

c² = 36 + 64

c² = 100

c = ± 10

Foci(– 8, – 2) & (12, – 2)

b² = 64 b = ± 8box points (2, – 10) & (2, 6)

Asymptotes

𝑦+2=±43

(𝑥− 2 )

•• •• •

•

•

x-term is positive: Horizontal

Assignment10-6 WB p275, 1-13 EOO + 10 Due 4/29

Conics Project Due Dates:Section 2 + 1 due TodaySections 3 & 4 + 1 & 2 due April 30

Foci (– 1, 3)

What is the standard form of the equation below? Give all key points of the conic section.

𝑥2+3 𝑦2+2 𝑥−18 𝑦− 8=0

¿

( 22 )

2

=1

1 +

(−62 )

2

=9

(−3 )2 +

(𝑥+1 )2+¿

(𝑥+1 )2

36+

3 (𝑦−3 )2

36=36  

36

(𝑥+1 )2

36+

(𝑦−3 ) 2

12=1

Ellipse

Center (– 1, 3)

a² = 36; a = ± 6

b² = 12; b =

c² = a² – b² c² = 36 – 12

c² = 24c

¿

; Vertices (5, 3) & (– 7, 3)

Co-Vertices (– 1, 3)

c =

3 ( 𝑦− 3 )2 36

State whether the graph is a circle, parabola, ellipse, or hyperbola.

1.

2.

3.

4.

7th Warm-Up 4/24

Parabola

Circle

Ellipse

Hyperbola

Conics Project Due Dates:Section 2 + 1 due Tomorrow April 25Sections 3 & 4 + 1 & 2 due April 30

10-6 Check Points I will check your answers.

Write equation in standard form.

Assignment10-6 WB p275, 1-13 EOO + 10

10-6 Check Points

Write equation in standard form.

I will check your answers.

10-6 Check Points

Analyze each equation. Complete each statement with the correct number.