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Chapter 10: Q. 28 (page 667)

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Foci at (0,-2)and (0,2); asymptote the liney=-x.

Short Answer

Expert verified

Equation of the hyperbola:y22-x22=1

Graph of the hyperbola:

Step by step solution

01

Step 1. Given information 

Hyperbola with foci at (0,-2)and (0,2); asymptote the liney=-x.

02

Step 2. Required to find 

Find the equation of the hyperbola. Graph the equation.

03

Step 3. Finding the equation of the hyperbola 

Given, hyperbola with foci at (0,-2)and (0,2); asymptote the line y=-x.

Comparing with standard form of hyperbola, y2a2-x2b2=1,b2=c2-a2;foci=(0,卤c);asymptotes,y=卤abx

We get,

role="math" localid="1646999459726" c=6,ab=1b2=c2-a2鈬�b2+a2=c2鈬�b2+b2=c2鈬�2b2=c2鈬�2b2=22鈬�b2=42鈬�b=卤2=a

Substituting aand bin the equation,

y22-x22=1

04

Step 4. Graphing the hyperbola 

Graph of the hyperbola:

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Most popular questions from this chapter

In Problems 63鈥� 66, graph each function by hand. Be sure to label any intercepts

f(x)=-1+x2

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

3x2-2xy+y2+4x+2y-1=0

Find the intercepts of the equation y2=16-4x2.

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

and equations of the parabola areA)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 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.13x2-63xy+7y2-16=0
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