Precalculus Chapter 10.4. Analytic Geometry 10 Hyperbolas 10.4.
9.5 Hyperbolas
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Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F 1 and F 2 , called the foci, is a constant. 9.5 Hyperbolas 9.5 Hyperbolas
description
9.5 Hyperbolas. Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F 1 and F 2 , called the foci, is a constant. 9.5 Hyperbolas. Transverse axis Conjugate Axis - PowerPoint PPT Presentation
Transcript of 9.5 Hyperbolas
Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F1
and F2, called the foci, is
a constant.
9.5 Hyperbolas9.5 Hyperbolas
Transverse axis
Conjugate Axis
Vertices
Co-vertices
Center
Foci
Asymptotes
(2a) length of V to V
(2b) length of CV to CV
Endpoints of TA
Endpoints of CA
Intersection of the 2 axes
Lie on inside of hyperbola
Horizontal Vertical
(When centered at the origin)
by x
a
ay x
b
9.5 Hyperbolas
Notes: a2 is always the denominator of the ________ term when the equation is written in standard form.
_________ axis can be longer or ____________ The length of the transverse axis is _________
The length of the conjugate axis is _________
a2 + b2 = c2
9.5 Hyperbolas
1st
Either shorter
2a
2b
2 2
2 21
x yOR
a b
2 2
2 21
x h y k
a b
2 2
2 21
y xOR
a b
2 2
2 21
y k x h
a b
Example 1:Write the standard equation of the hyperbola with vertices (-4,0) and (4,0) and co-vertices (0, -3) and (0, 3). Sketch the graph.
Example 2: Write the standard equation of the hyperbola with V(-7, 0) (7, 0) and CV (0,-4) (0, 4).
Example 3: Write the standard equation of the hyperbola with F (-1, 1) (5, 1) and V (0, 1) (4, 1).
Example 4: Write the standard equation of the hyperbola with F (3, -3) (3, 7) and V (3, -1) (3, 5).
Don’t forget! x and h are BFFs!So are y and k! Don’t split them up!
Example 5:Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola.
149
22
xy
Example 6: The equation x2 – y2 –6x –10y –20 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.
Example 7: The equation –2x2 + y2 + 4x + 6y + 3 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.
Example 8: The equation 4x2 – 25y2 – 8x + 100y – 196 = 0 represents a hyperbola. Write the standard equation of the hyperbola. Give the coordinates of the center, vertices, co-vertices, and foci. Then graph the hyperbola.
