Question
Asked Nov 18, 2019
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П
I
YA
у.
4
2
X
Ш
yA
у
IV
2
1
2
х
х
9-26 Graphing Hyperbolas An equation of a hyperbola is
given. (a) Find the vertices, foci, and asymptotes of the hyper-
bola. (b) Determine the length of the transverse axis. (c) Sketch a
graph of the hyperbola.
1,2
2
+t
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П I YA у. 4 2 X Ш yA у IV 2 1 2 х х 9-26 Graphing Hyperbolas An equation of a hyperbola is given. (a) Find the vertices, foci, and asymptotes of the hyper- bola. (b) Determine the length of the transverse axis. (c) Sketch a graph of the hyperbola. 1,2 2 +t

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y A
21
UOke
y2
10.
= 1
16
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y A 21 UOke y2 10. = 1 16

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Expert Answer

Step 1

Given,

An equation of a hyperbola is

=1
16
9
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=1 16 9

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Step 2

An equation can be written as

=1
32 42
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=1 32 42

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Step 3

a)

...
=1 with standard equation of hyperbola-
a2
1, we get
Compare
32
a 3, b 4
The vertex and foci of the hyperbola with center at origin is (0,ta) and (0,tc) respectively
where c a +b2 .
= lis (0,3) and (0,-3) and foci are
16
Therefore, the vertex of hyperbola
9
(0,#/3 +4°) =(0,+5)
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=1 with standard equation of hyperbola- a2 1, we get Compare 32 a 3, b 4 The vertex and foci of the hyperbola with center at origin is (0,ta) and (0,tc) respectively where c a +b2 . = lis (0,3) and (0,-3) and foci are 16 Therefore, the vertex of hyperbola 9 (0,#/3 +4°) =(0,+5)

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