Download Pre-AP Algebra 2 Wednesday, August 18

Algebra 2
Wednesday, May 24,
2017
 Goal(s)
 Write
equations of hyperbolas given
vertices and foci
 Write equations of hyperbolas in
standard form
Equations of a Hyperbola
Standard Equations (center at origin):
Horizontal transverse
axis: x2
y2
2
a



2
b
Vertical transverse axis:
y2
1
a2
(a,0) and (-a,0) are
the vertices
b
Asymptotes: y   x
a



x2
b2
1
(0,a) and (0,-a) are
the vertices
a
Asymptotes: y  
•Foci are c units from the center on the
major axis, where c2=a2+b2
b
x

Writing Equations of
Hyperbolas
Vertices:
 ‘a’
units from the center
 (a,0) & (-a,0)  horizontal (a2 and x-term
written first)
 (0,a)
& (0,-a)  vertical (a2 and y-term
written first)

Foci:
 ‘c’
units from the center
 c2 = a2 + b2
Parts of a Hyperbola

The constant must = 1

If the constant is not = 1, divide all terms
by the constant

If the coefficients are not = 1, rewrite
multiplication as division by a fraction