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Chapter 10: Q. 33 (page 668)

In Problems 29鈥�36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation by hand. Verify your graph using a graphing utility.y2-9x2=9

Short Answer

Expert verified

Center:(0,0)Transverseaxis:y-axisVertices:(0,卤3)Foci:(0,卤10)Asymptotes:y=卤3x

Graph of the equation is:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola, y2-9x2=9

Writing the equation in standard form,

y29-9x29=1鈬�y29-x2=1

02

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

Comparing the given equation with standard form, y2a2-x2b2=1,b2=c2-a2

We get,

a=3,b=1,c=卤a2+b2鈬�c=卤32+12鈬�c=卤9+1鈬�c=卤10

Center:(0,0)Transverseaxis:y-axisVertices:(0,卤a)=(0,卤3)Foci:(0,卤c)=(0,卤10)Asymptotes:y=卤abx鈬�y=卤31x鈬�y=卤3x

03

Step 3. Graph of the equation

Graph of the equation is:

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