Bell Work
Write the equation of a hyperbola centered at
(0, 0) that opens up and down.
Then, graph your equation.
Translations of Hyperbolas
Hyperbolas centered at (h,k)
Standard Equation
(𝑥−ℎ)2
𝑎2
−
(𝑦−𝑘)2
𝑏2
=1
(𝑦−𝑘)2
𝑎2
−
Pythagorean Relation
𝑐 2 = 𝑎2 + 𝑏2
𝑏
±
𝑎
𝑎
±
𝑏
Asymptotes
y=
𝑥−ℎ +𝑘
y=
(𝑥−ℎ)2
𝑏2
=1
𝑥−ℎ +𝑘
Example
Sketch the hyperbola.
𝑥2
16
−
(𝑦−3)2
9
=1
Example
Find the center, vertices, and foci of the hyperbola.
(𝑥 + 4)2 (𝑦 + 6)2
−
=1
16
25
Example – You Try
Find the center, vertices, and foci of the hyperbola.
(𝑦 − 1)2 (𝑥 + 5)2
−
=1
64
25
Example
Find an equation in standard form for the
hyperbola that satisfies the given conditions.
Transverse axis endpoints (2,3) and (2,-1),
conjugate axis length 6
Example
Find an equation in standard form for the
hyperbola that satisfies the given conditions.
Transverse axis endpoints (-1,3) and (5,3), slope
of one asymptote 4/3
Homework
8.3 (pg. 609) #9,10,15,16,32,33,40,42