1. 9.5A Graph Hyperbolas
Algebra II

2. Hyperbolas
Like an ellipse but instead of the sum of distances it is the difference
A hyperbola is the set of all points P such that the differences from P to two fixed points, called foci, is constant
The line thru the foci intersects the two points (the vertices)
The line segment joining the vertices is the transverse axis, and it’s midpoint is the center of the hyperbola.
Has 2 branches and 2 asymptotes
The asymptotes contain the diagonals of a rectangle centered at the hyperbolas center

3. (0,b) (0,-b) Asymptotes Vertex (a,0) Vertex (-a,0) Focus Focus
This is an example of a horizontal transverse axis

4. Vertical transverse axis

5. Standard Form of Hyperbola w/ center @ origin
Equation
Transverse Axis
Asymptotes
Vertices
Horizontal
y=+/- (b/a)x
(+/-a,o)
Vertical
y=+/- (a/b)x
(0,+/-a)
Foci lie on transverse axis, c units from the center c2 = a2+b2

6. Ex. 1)Graph Write in standard form (divide through by 144) a=4 b=3
transverse axis is vertical & vertices are
(0,4) & (0, -4) Plot other pts from b value
(3,0) , (-3,0) to make rectangle
Draw a rectangle centered at the origin.
Draw asymptotes.
Draw hyperbola with foci.

7. Graph

8. Ex. 2 Graph

9. 9.5B Write Equations of Hyperbolas
Algebra II

10. Ex. 1)Write the equation of a hyperbola with foci (0,-3) & (0,3) and vertices (0,-2) & (0,2).
Vertical because foci & vertices lie on the y-axis
origin because f & v are equidistant from the origin
Since c=3 & a=2, c2 = b2 + a2
9 = b2 + 4
5 = b2
+/-√5 = b

11. Standard Form of Hyperbola w/ center @ origin
Equation
Transverse Axis
Asymptotes
Vertices
Horizontal
y=+/- (b/a)x
(+/-a,o)
Vertical
y=+/- (a/b)x
(0,+/-a)
Foci lie on transverse axis, c units from the center c2 = a2+b2

12. Ex. 2 Write an equation of the hyperbola with the given foci & vertices
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13. Assignment