(a) Find the vertices, foci and asymptotes of the hyperbola and
sketch its graph 9y^2 −...
(a) Find the vertices, foci and asymptotes of the hyperbola and
sketch its graph 9y^2 − 4x^2 − 72y + 8x + 176 = 0. (b) Find the
vertex, focus and directrix of the parabola and sketch its graph
6y^2 + x − 36y + 55 = 0.
Find the center, vertices, foci, and the equations of the
asymptotes of the hyperbola. (If an answer does not exist, enter
DNE.)
x2 − 2.25y2 + 22.5y − 92.25 = 0
Find the equation of the hyperbola with:
(a) Foci (1, −3) and (1, 5) and one vertex (1, −1).
(b) Vertices (2, −1) and (2, 3), and asymptote x = 2y.
Consider the set of points described by the equation 16x2 −4y2
−64x−24y+19=0.
(a) Show that the given equation describes a hyperbola and find
the center of the hyperbola.
(b) Determine the equations of the directrices as well as the
eccentricity.
1. Find the standard form of the equation of the hyperbola
satisfying the given conditions. Foci at (-5,0) and (5,0); vertices
at (1,0) and (-1,0).
2. Find the standard form of the equation of the hyperbola
satisfying the given conditions. Foci at (0,-8) and (0,8); vertices
at (0,2) and (0,-2).
An equation of a hyperbola is given.
y^2/36 - x^2/64 = 1
(a) Find the vertices, foci, and asymptotes of the hyperbola.
(Enter your asymptotes as a comma-separated list of equations.)
vertex
(x, y)
=
(smaller y-value)
vertex
(x, y)
=
(larger y-value)
focus
(x, y)
=
(smaller y-value)
focus
(x, y)
=
(larger y-value)
asymptotes
(b) Determine the length of the transverse axis.
(c) Sketch a graph of the hyperbola.
An equation of a hyperbola is given.
25x2 − 16y2 = 400
(a) Find the vertices, foci, and asymptotes of the hyperbola.
(Enter your asymptotes as a comma-separated list of equations.)
vertex
(x, y)
=
(smaller x-value)
vertex
(x, y)
=
(larger x-value)
focus
(x, y)
=
(smaller x-value)
focus
(x, y)
=
(larger x-value)
asymptotes
(b) Determine the length of the transverse axis.
(c) Sketch a graph of the hyperbola.
Find the vertical asymptotes (if any) of the graph of the
function. (Use n as an arbitrary integer if necessary. If
an answer does not exist, enter DNE.)
h(x) =
x2 − 9
x3 + 3x2 − x − 3
(line in the middle of both functions is a division line)
Sketch the graph of f by hand and use your sketch to
find the absolute and local maximum and minimum values of
f. (Enter your answers as a comma-separated list. If an
answer does not exist, enter DNE.)
f(t) = 2 cos(t), −3π/2 ≤ t ≤ 3π/2
absolute maximum value
absolute minimum value
local maximum value(s)
local minimum value(s)
Sketch the graph of f by hand and use your sketch to
find the absolute and local maximum and minimum values of
f. (Enter your answers as a comma-separated list. If an
answer does not exist, enter DNE.)
f(x) =
x2
if −1 ≤ x ≤ 0
2 −
3x
if 0 < x ≤ 1
absolute maximum value
absolute minimum value
local
maximum value(s)
local
minimum value(s)
Sketch the graph of f by hand and use your sketch to find the
absolute and local maximum and minimum values of f. (If an answer
does not exist, enter DNE.) Absolute maximum, absolute minimum,
local maximum, local minimum.
f(x) = ln 3x, 0 < x ≤ 7
Find the absolute maximum and absolute minimum values of f on
the given intervals(absolute maximum, absolute minimum).
f(x) = 6x^3 − 9x^2 − 216x + 3, [−4, 5]
f(x) = x/x^2 −...