Download 10.4 Hyperbolas

10.4
Hyperbolas
JMerrill 2010
Definition
A hyperbola is the set of all points in a plane, the
difference of whose distances from two distinct
fixed point (foci) is a positive constant.
Equations of Hyperbolas
y k 
b
(x  h )
a
y k 
a
(x  h )
b
Writing the Equation

Find the equation of the hyperbola with
vertices(-3, 2), (3, 2) and foci (-5, 2), (5, 2).
Graph.
y  3

x

1
9
16
2
2
Find and Graph the Hyperbola


State the direction of the transverse axis, sketch a
graph and find the center, the vertices, and the
foci.
2
2
transverse axis:
◦ vertical

center:
◦ (-2, 1)

vertices:
◦ (-2, 3), (-2, -1)

foci:
◦ ( 2,1  13)
( y  1) ( x  2)

1
4
9
Writing the Equation in Standard
Form – You Try
Given 4x2 – 3y2 + 8x + 16 = 0
 You must complete the square

y
(x  1)

1
4
3
2
2
Eccentricity
c
e
a
The same formula
applies to both
ellipses and hyperbolas.
 If the eccentricity is large, the branches of
the hyperbola are nearly flat.
 If the eccentricity is close to 1, the
branches are more narrow.
