How do you know whether to put y2/a first or x2/a first?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 32E
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How do you know whether to put y2/a first or x2/a first?

9.3: Hyperbolas
Chapter 9: Topics in Analytic Geometry
Write the equation of the hyperbola in standard form, identify the center, vertices, foci, and slope of the asymptotes,
then sketch the hyperbola.
2
1. 4y²-9x² = 36
2
36 36 36
x² 2
4
=1
²a=3²/16 = 2
¥²
C:(0,0)
V: (0,3)
(0,3).
F: (0,₂413) ←
(0₁-√13)
(2= a² + b²
9+4
C=√13
за
2. b
m asymps: ±
2. 16x²-9v² +64x+18y-89=0
-6 -4 --2
Ay
4
6
X
Transcribed Image Text:9.3: Hyperbolas Chapter 9: Topics in Analytic Geometry Write the equation of the hyperbola in standard form, identify the center, vertices, foci, and slope of the asymptotes, then sketch the hyperbola. 2 1. 4y²-9x² = 36 2 36 36 36 x² 2 4 =1 ²a=3²/16 = 2 ¥² C:(0,0) V: (0,3) (0,3). F: (0,₂413) ← (0₁-√13) (2= a² + b² 9+4 C=√13 за 2. b m asymps: ± 2. 16x²-9v² +64x+18y-89=0 -6 -4 --2 Ay 4 6 X
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Follow-up Question

How do you know that y2/a has to come first?

Ly-0) 2
(3)²
(x-01²
(2)2
=1
Transcribed Image Text:Ly-0) 2 (3)² (x-01² (2)2 =1
Solution
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Follow-up Question

How would you know which equation to use if you were just given this problem?

Write the equation of the hyperbola in standard form, identify the center, vertices, foci, and slope of the asymptotes,
then sketch the hyperbola.
2
1. 4y²-9x² = 36
Transcribed Image Text:Write the equation of the hyperbola in standard form, identify the center, vertices, foci, and slope of the asymptotes, then sketch the hyperbola. 2 1. 4y²-9x² = 36
Solution
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