Aim #57 and 58: How do we analyze the equation of hyperbolas?
HW Packet Due Friday (Hopefully Monday!)
Quiz (Aims 55-58) Monday
Test (Aims 52-58) Wednesday
Do Now:
Determine which type of conic section is represented by the following
equations
1.
2x2 + 2y2 + 4x + 6y ­ 12 = 0
2.
2y2 + x2 + 4x + 6y ­ 12 = 0
3.
2y2 + 4x + 6y ­ 12 = 0
Aim #57 and 58: How do we analyze the equation of hyperbolas?
HW Packet Due Monday
Quiz Tuesday and Test Thursday
Do Now:
Determine which type of conic section is represented by the following
equations
1.
2.
3.
4.
Hyperbola
A hyperbola is the set of all points P in the plane, the
difference of whose distances from two fixed points, called
the foci, is a constant.
For a given hyperbola, the following is true:
a2 + b2 = c2
General Form
Equation of Asymptotes
Analyze the equation by finding the center, foci, vertices, asymptotes
and transverse axis. Then, sketch the graph.
25
Transverse Axis:
A=
B=
Center:
Vertices:
Foci:
Asymptotes:
Find an equation of the hyperbola with center at the origin, one focus
at (3, 0) and one vertex at (-2, 0). Graph the equation.
Analyze the equation by finding the center, foci, vertices, asymptotes
and transverse axis. Then, sketch the graph.
Transverse Axis:
A=
B=
Center:
Vertices:
Foci:
Asymptotes:
Find an equation for the hyperbola with center at (1, -2), one focus
at (4, -2) and one vertex at (3, -2). Graph the equation by hand.
Analyze the equation by finding the center, foci, vertices and
transverse axis.
Analyze the following hyperbola by finding the center, foci, vertices
and equations of the two asymptotes.
Determine the equation of a hyperbola with vertices at (-4, 0) and
(4, 0) that has an asymptote defined by the line y = 2x.
Find an equation for the hyperbola with vertices at (1, -3) and
(1, 1) which has an asymptote defined by the line y + 1 = 2/3(x - 1).