BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.9, Problem 28E
To determine

To graph: The circle (y1)2+x2=1 by solve for y .

Expert Solution

Explanation of Solution

Given information:

The equation of circle (y1)2+x2=1 .

Graph:

The graph of circle (y1)2+x2=1 by solving for y .

Subtract x2 from the equation of circle,

  (y1)2+x2x2=1x2(y1)2=1x2

Take under root on both side of the equation,

  y1=±1x2

Add 1 on the equation,

  y1+1=1±1x2y=1±1x2

From the two equations graph of circle is described:

  y=1+1x2,y=11x2

The graph of the equation y=1+1x2 represents upper half of the circle because y is always greater than or equal to 1.

  1+1x211x201x2±1x

So, the values of x is less than or equal to ±1 .

Thus, the graph appropriate in the [1,1]×[0,2] viewing rectangle

The graph of the equation y=1+1x2 can be sketched using the table,

    xy
    02
    11
    121+34

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 28E , additional homework tip  1

The graph of the equation y=11x2 represents upper half of the circle because y is always less than or equal to 1.

  11x211x201x20±1x

So, the values of x is greater than or equal to ±1 .

Thus, the graph appropriate in the [-1,1]×[0,1] viewing rectangle

The graph of the equation y=11x2 can be sketched using the table,

    xy
    00
    11
    12134

The graph of equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 28E , additional homework tip  2

The graph of both equations in same figure is provided below,

Thus, the graph appropriate in the [-1,1]×[0,2] viewing rectangle

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.9, Problem 28E , additional homework tip  3

Interpretation:

The graph of an equation in a viewing screen is a viewing rectangle.

The x -values to range from a minimum value of xmin =a to a maximum value of xmax =b

The y -values to range from minimum value of ymin =c to a maximum value of ymax =d

Then, the display portion of the graph lies in the rectangle [a,b]×[c,d]={(x,y)|axb,cyd}

The graph of the equation y=1+1x2 represents upper half of the circle appropriate in the [1,1]×[0,1] viewing rectangle.

The graph of the equation y=11x2 represents upper half of the circle appropriate in the [1,1]×[0,2] viewing rectangle

The graph of the equation (y1)2+x2=1 represents circle in the [1,1]×[0,2] viewing rectangle.

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