2. A hyperbola is the set of all points in the
plane in which the difference of the distances
from two distinct fixed points is constant.
The foci is the constant, that if F1 and F2 are
the foci of the hyperbola and P and Q are any
two points on the hyperbola.
Foci Formula: |PF₁ – PF₂ |= |QF₁ – QF₂ |
3. Center- the midpoint of the line segment
whose endpoints are the foci.
Formula for center: F₁F₂/2
Vertex- the point on each branch of the
hyperbola that is nearest to the center.
4. Asymptotes- The lines that the curve
approaches as it recedes from the center. As
you move further out along the branches, the
distance between points on the hyperbola
and the asymptotes approaches zero.
Transverse axis- the line segment connecting
the vertices. Also has a length of 2a units.
Conjugate axis- the segment perpendicular
to the transverse axis through the center.
Also has a length of 2b units.
5. For a hyperbola the relationship among a, b,
and c is represented by a2 + b2 =c2. The
asymptotes contain the diagonals of the
rectangle which the diagonals meet coincides
with the center of the hyperbola.
C > a for the hyperbola.
For standard for of a hyperbola with it’s
origin as its center can be derived from the
foci are on the x- axis at (c,0) and (-c,0) and
the coordinates of any point on the hyperbola
are (x,
6.
7. Distance formula: |√((x + c)2 + y2 )- √((x +
c)2 + y2 )= |c + a – (c –a)|
Hyperbola Formula: |PF2 –PF1 | = |VF2 – VF1|
If the foci are on the y-axis, the equation is
y2/a2 – x2 /b2 = 1
The standard form of the equation of the
hyperbola with center other than the origin is
a translation of the parent graph to a center
at (h, k).
