Chapter 9, Problem 8RE

(a)

To determine

To find:The equationin rectangular coordinates for given polar coordinate.

Answer to Problem 8RE

The equation in rectangular coordinates is $x^2+y^2=25$ .

Explanation of Solution

Given information:

The given polar equation is $r=5$ .

Calculation:

Squaring on both sides of the equation $r=5$ .

  $r^2=25$

Substitute $x^2+y^2$ for $r^2$ to get an equation in $x$ and $y$ .

  $x^2+y^2=25$

Therefore, the equation in rectangular coordinates is $x^2+y^2=25$ .

(b)

To determine

To graph:For the equation.

Explanation of Solution

Given information:

The equation is $x^2+y^2=25$ .

Graph:

The equation $x^2+y^2=25$ is of the form $x^2+y^2=r^2$ .

The graph of $r=5$ is a circle with center at the pole and radius $5$ .

The graph for the equation is shown in figure (1).

  

Figure (1)

Interpretation:Graph for the equation $x^2+y^2=25$ is shown in figure (1).