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Guided Notes for Unit 4-4: Hyperbola Learning Target: I will graph hyperbolas.
HYPERBOLA TERMS
a
C=(h , k)
EQUATION FORM
CENTER
VERTICES
CO-VERTICES
ASYMPTOTES
(h, k )
(h, k ± b )
(h ± a , k)
b
Vertex
Co-vertex
Co-vertex
1b
)ky(
a
)hx(2
2
2
2
Vertex)( hx
a
bky
The “Butterfly”
HYPERBOLA TERMS
a
C=(h , k)
EQUATION FORM
CENTER
VERTICES
CO-VERTICES
ASYMPTOTES
(h, k )
(h ± b, k)
(h, k ± a )
b
Vertex
Co-vertex
Co-vertex
1b
)hx(
a
)ky(2
2
2
2
Vertex
)( hxb
aky
The “Hourglass”
Example 1 Graph 4x2 – 16y2 = 64.
4x2 – 16y2 = 64
– = 1 Rewrite the equation in standard form. x 2
16y 2
4
Since a2 = 16 and b2 = 4, a = 4 and b = 2.
The equation of the form , so
Step 1: Graph the vertices. Since the transverse axis is horizontal, the vertices lie on the x-axis. The coordinates are (±a, 0), or (±4, 0).
Step 2: Use the values a and b to draw the central “invisible” rectangle. The lengths of its sides are 2a and 2b, or 8 and 4.
Example 1 Graph 4x2 – 16y2 = 64.
Step 3: Draw the asymptotes. The equations of the asymptotes are
, which comes out to be and the asymptotes contain the diagonals of the central rectangle.
Step 4: Sketch the branches of the hyperbola through the vertices so they approach the asymptotes.
Graph and Label b) Find coordinates of vertices,
covertices
Center = (-5,-2) Butterfly shape since the x
terms come first Since a = 2 and b = 3 Vertices are 2 points left and
right from center (-5 ± 2, -2) CoVertices are 3 points up and
down (-5, -2 ± 3)
19
)2y(
4
)5x( 22
• a) GRAPH• Plot Center (-5,-2)• a = 2 (go left and right)• b = 3 (go up and down)
Graph and Label b) Find coordinates of vertices,
covertices,
Center = (-1,3) Hourglass shape since the y
terms come first Since a = 2 and b = 4 Vertices are 2 points up and
down from center (-1, 3 ± 2) Covertices are 3 points left and
right (-1 ± 4, 3)
116
)1x(
4
)3y( 22
• a) GRAPH• Plot Center (-1,3)• a = 2 (go up and down)• b = 4 (go left and right)
Assignment
Pg. 629
#16-19
