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Chapter 10: Q. 32 (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.4y2-x2=16

Short Answer

Expert verified

Center:(0,0)Transverseaxis:y-axisVertices:(0,卤2)Foci:(0,卤25)Asymptotes:y=卤12x

Graph of the equation:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola, 4y2-x2=16

Writing the equation in standard form,

4y216-x216=1鈬�y24-x216=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=2,b=4,c=卤b2+a2鈬�c=卤42+22鈬�c=卤16+4鈬�c=卤20鈬�c=卤25

Center:(0,0)Transverseaxis:y-axisVertices:(0,卤a)=(0,卤2)Foci:(0,卤c)=(0,卤25)Asymptotes:y=卤abx鈬�y=卤24x鈬�y=卤12x

03

Step 3. Graph of the equation

Graph of the equation is:

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