1. Chapter 10 Section 5 Hyperbola
Algebra II
Chapter 10 Section 5
Hyperbola

2. Hyperbola
The set of all points that have the difference of the distance to 2 focus points is a given constant

3. Parts of a hyperbola
Asymptotes
Foci
Transverse Axis
Vertices

4. Standard Form of an Hyperbola
If a & b > 0 the Transverse axis is Horizontal
If a & b < 0 the Transverse axis is Vertical

5. Put into standard Form

6. Put into standard Form

7. In standard form
The +-value for a (square root of the denominator of x2) are the vertex’s x if the Transversal Axis is horizontal, values (-a,0) and (a,0)
The +-value for b (square root of the denominator of y2) are the vertex’s y if the Transversal Axis is Vertical, values (0,-b) and (0,b)

8. To find the Asymptote

9. Find the Asymptotes and Vertices

10. (4,0) and (-4,0) a = 4 b = 5 Horizontal Transverse Axis
So Vertices are at +- (a,0)
(4,0) and (-4,0)
Asymptotes are at

12. Given a vertex at (-3, 0) and an asymptote of y = 4x
Find the equation of hyperbola

13. Foci Foci are always on the transverse axis
Foci are equidistant from the minor axis
The distances to a focus from the origin is equal to the distance along the asymptote, with a coordinate = to the vertex’s non zero coordinate

14. Find the focus of an Hyperbola with its center on the origin
If c is the distance from the center to the focus
Find c using c2 = a2 + b2
if your transverse axis is Horizontal your foci are at (+-c ,0)
if your transverse axis is Vertical your foci are at (0 ,+-c)

16. Find the foci of
a & b are + so we have a horizontal Transverse axis (y = 0) c2 = a2 + b2 c2 = c2 = 25 c = 5 So the coordinates of the foci are at (5,0) and (-5,0)

17. Find the Foci

18. Find the equation given a vertex and a focus
Find the other vertex using c2 = a2 + b2
Substitute in the 2 values you know and solve for the 3rd
Remember the foci will lie along the Transverse axis
c is the distance of the focus to the origin
Once you have the 2 vertices, take the square roots to get a and b & substitute them in

19. Given a focus of (10,0) and a vertex at (-6,0) find the equation of the Hyperbola
The transverse axis is Horizontal since the vertex and focus lie on the x axis
Since the vertex is at (0,-6) a2 = 36
Since the focus is at (0,10) c2 = 100
Substitute a2 and c2 into a2 + b2 = c2 and solve for b
36 + b2 = 100 b2 = 64 b= 8
Substitute a2 & b2 into
To get

20. Given a focus of (13,0) and a vertex at (5,0) find the equation of the ellipse

21. Do Now!
Page 566 Problems
2 – 18 even, find the vertex, foci and asymptotes as well as sketch a graph
23 – 26 all
30, 31, 36, 40, 42,