Question

Convert the equations given in polar coordinates to equations in rectangular coordinates.

$r=k$for each positive integer k less than 10.

Short answer

The equation is:

$x^2+y^2=k^2$.

Step-by-step solution

Step 1. Given information

Polar form of equation:

$r=k$,$k<10$and all positive integers.

Step 2. Convert into rectangular form.

As we know that

$r=\sqrt{x^2+y^2}$

so,

$$\begin{gathered} r=k \\ \sqrt{x^2+y^2}=k \\ {x}^2+y^2=k^2 \end{gathered}$$