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Chapter 10: Q. 29 (page 668)

In Problems 29–36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.x225-y29=1

Short Answer

Expert verified

Center:(0,0)Transverseaxis:x-axisVertices:(±5,0)Foci:(±34,0)Asymptotes:y=±35x

Graph of the equation is:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola,x225-y29=1

02

Step 2. Finding the center, transverse axis, vertices, foci, and asymptotes of hyperbola

Comparing the given equation with standard form, x2a2-y2b2=1,b2=c2-a2

We get,

role="math" localid="1647141709647" a=5,b=3,c=±b2+a2⇒c=±32+52⇒c=±9+25⇒c=±34

Center:(0,0)Transverseaxis:x-axisVertices:(±a,0)=(±5,0)Foci:(±c,0)=(±34,0)Asymptotes:y=±bax⇒y=±35x

03

Step 3. Graph of the equation

Graph of the equation is:

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Most popular questions from this chapter

Find an equation for each ellipse. Graph the equation by hand.

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True or False

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