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Chapter 10: Q. 30 (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.y216-x24=1

Short Answer

Expert verified

Center:(0,0)Transverseaxis:y-axisVertices:(0,卤4)Foci:(0,卤25)Asymptotes:y=卤2x

Graph of the equation is:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola,y216-x24=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,

role="math" localid="1647141861700" a=4,b=2,c=卤a2+b2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4)Foci:(0,卤c)=(0,卤25)Asymptotes:y=卤abx鈬�y=卤42x鈬�y=卤2x

03

Step 3. Graph of the equation

Graph of the equation is:

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Most popular questions from this chapter

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:

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