Download Algebra II Sec. 10.5 notes

Algebra II Sec. 10.5 notes
I.
Objective: To write & graph the equation of a hyperbola.
Hyperbola – the set of all points in a plane
such that the absolute value of the
difference of the distances from two fixed
points (Foci) is constant.
II.
Standard form of an equation of a hyperbola:
𝑥2
𝑎2
−
𝑦2
𝑏2
=1
Vertices & Foci are on
x -axis
Asymptotes
𝑏
𝑦=± 𝑥
𝑎
2
2
2
=
𝑎
+
𝑏
𝑐
𝑎2 is first
𝑦2 𝑥2
−
=1
𝑎2 𝑏 2
Vertices & Foci are on
y -axis
Asymptotes
𝑎
𝑦=± 𝑥
𝑏
a = distance from center to the vertices (endpoints of the transverse axis)
b = distance from center to the endpoints of the conjugate axis
c = distance from center to the Foci (same axis as the transverse axis)
Ex1 Write an equation of a hyperbola where a = 3 & b = 4. Assume that the
transverse axis is horizontal.
Ex2 & Ex3 Name what’s listed & then graph the hyperbola.
Ex2
𝑥2
36
−
𝑦2
64
=1
Vertices ____________
Foci ______________
Asymptotes ___________
Ex3
25𝑦 2 − 16𝑥 2 = 400
Vertices ____________
Foci ______________
Asymptotes ___________
Assignment:
p650: 9-210dd, 25, 27