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Chapter 10: Q. 34 (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.x2-y2=4

Short Answer

Expert verified

Center:(0,0)Transverseaxis:x-axisVertices:(卤2,0)Foci:(卤22,0)Asymptotes:y=卤x

Graph of the equation is:

Step by step solution

01

Step 1. Given information 

Equation of hyperbola, x2-y2=4

Writing the equation in standard form,x24-y24=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,

a=2,b=2,c=卤a2+b2鈬�c=卤22+22鈬�c=卤4+4鈬�c=卤8鈬�c=卤22

role="math" localid="1647143921159" Center:(0,0)Transverseaxis:x-axisVertices:(卤a,0)=(卤2,0)Foci:(卤c,0)=(卤22,0)Asymptotes:y=卤bax鈬�y=卤22x鈬�y=卤x

03

Step 3. Graph of the equation

Graph of the equation is:

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3x2+2xy+y2+4x-2y+10=0

The graph of a parabola is given. Match each graph to its equation.

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

10x2-12xy+4y2-x-y-10=0

The graph of a parabola is given. Match graph to its equation.

A)y2=4xC)y2=-4xE)(y-1)2=4(x-1)G)(y-1)2=-4(x-1)B)x2=4yD)x2=-4yF)(x+1)2=4(y+1)H)(x+1)2=4(y+1)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (3,0); vertex at(1,0).
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