Activity II. A. Find the following: 1. Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation 16y -x = 16. 2. Find the equation of a hyperbola that has the y axis as the transverse axis, a center at (0, 0) and passes through the points (0, 5) and (2, 5v2). 3. Find the equation of a hyperbola whose vertices are at (0, -3) and (0, 3) and has a focus at (0 ,5).
Activity II. A. Find the following: 1. Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation 16y -x = 16. 2. Find the equation of a hyperbola that has the y axis as the transverse axis, a center at (0, 0) and passes through the points (0, 5) and (2, 5v2). 3. Find the equation of a hyperbola whose vertices are at (0, -3) and (0, 3) and has a focus at (0 ,5).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Activity II.
A. Find the following:
1. Find the transverse axis, the center, the foci and the vertices of the hyperbola
whose equation 16y2-x2 16.
2. Find the equation of a hyperbola that has the y axis as the transverse axis, a center
at (0, 0) and passes through the points (0, 5) and (2, 5v2).
3. Find the equation of a hyperbola whose vertices are at (0, -3) and (0, 3) and has
a focus at (0, 5).
B. Complete the table below.
Table 1. Where the center of the hyperbola is at (h, k).
Equation
Vertices
Foci
Ends
of Asymptotes
Conjugate Axis
(x- h) (y- k)²
= 1
(h tc, k)
b
y = +-(x- h) + k
a?
b2
(h, k ta)
(h +b, k)
Table 2.
Equation
Vertices
Foci
Ends
of Asymptotes
Conjugate Axis
(0土)
(±b,0)
(±a,0)
y? x2
0, (±c)
Activity III. Solve the following. (Show your solution)
1. Find the asymptotes of the parabolas given by the equations:
x? y?
1
4
36
y? – 49x? = 49
2. Find the equation of a hyperbola with vertices at (0, -7) and (0, 7) and asymptotes
given by the equations y 3x and y = - 3x.
3. Write the equation of a hyperbola with the x axis as its transverse axis, point (3, 1)
lies on the graph of this hyperbola and point (4 , 2) lies on the asymptote of this
hyperbola.
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