The conic sections and application in real world

1. HYPERBOLA

2. What is Hyperbola?
- is the set of all points, whose
distances from two fixed points
differbyacertainconstant.
- can be formed by intersecting a
double-napped cone with a plane in
such a manner that both nappes are
intersected

3. Parts of Hyperbola
The two fixed points are called the
foci (plural of focus) of the
hyperbola.
- c unitsawayfromthecenter
The line segment containing both
foci of a hyperbola whose endpoints
are both on the hyperbola is called
the transverse axis.

4. The endpoints of the transverse
axis are called the vertices of the
hyperbola.
-collinearwith thecenterand foci
The point halfway between the foci
(the midpoint of the transverse
axis)is the center.
The line segment perpendicular to
the transverse axis is the conjugate
axis.

5. The asymptotes of the hyperbola
are two lines passing through the
center which serve as guide in
graphing thehyperbola.
To help us sketch the asymptotes,
we point out that the asymptotes
are the extended diagonals of the
auxiliary rectangle.

6. Parts of Hyperbola

7. Application of
Hyperbola in Real
World

12. Standard
Equation of a
Hyperbola

15. FormulaForAsymptotes:
C(0,0)
C(h,k)

16. Sample
Problem

17. 1) Determine the foci, vertices, and
asymptotes of the hyperbola with the
equation
2) Find the standard equation of the
hyperbola whose foci are F1(-5,0) and F2
(5,0), such that for any point on it, the
absolute value of the difference of its
distancesfromthefociis6.

18. Give the coordinates of the center, foci,
vertices,andasymptotesofthehyperbola
with the given equation. Sketch the
graph, and include these points and lines,
the transverse and conjugate axes, and
theauxiliaryrectangle
3)
4) 4