warm-up 4/24
DESCRIPTION
Warm-Up 4/24 . Parabola. 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. - PowerPoint PPT PresentationTRANSCRIPT
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 = – b²64 = 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 = 24
c
¿
; 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.