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Chapter 12: Q.2 (page 988)

Level curves: Sketch the level curves fx,y=cof the following functions forc=-3,-2,-1,0,1,2,3

fx,y=y2-x2

Short Answer

Expert verified

The level curves is shown in the figure

Step by step solution

01

Step 1. Given Information

The given functionfx,y=y2-x2andc=-3,-2,-1,0,1,2,3

02

Step 2. For c=0

fx,y=cy2-x2=0y=卤x

This represent identity function,

03

Step 3. For c=1

y2-x2=1

Represent hyperbola with foci0,卤2

04

Step 4. For c=-1

y2-x2=-1

or x2-y2=1

represent hyperbola with foci卤2,0

05

Step 5. For next values of c

06

Step 6. Level Curves

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