Q. 56 - Calculus

Question

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

$r=1,r=-2,r=3$

Step-by-Step Solution

Answer

The rectangular form of equations are:

$$\begin{gathered} x^2+y^2=1 \\ {x}^2+y^2=4 \\ {x}^2+y^2=9 \end{gathered}$$

Step 1. Given information

The polar form of equations:

$$\begin{gathered} r=1 \\ r=-2 \\ r=3 \end{gathered}$$

Step 2. Convert polar form into the rectangular form.

As we know that $r=\sqrt{x^2+y^2}$

So 

$$\begin{gathered} r=1 \\ \sqrt{x^2+y^2}=1 \\ {x}^2+y^2=1 \end{gathered}$$

$$\begin{gathered} r=-2 \\ \sqrt{x^2+y^2}=-2 \\ {x}^2+y^2={(-2)}^2 \\ {x}^2+y^2=4 \end{gathered}$$

$$\begin{gathered} r=3 \\ \sqrt{x^2+y^2}=3 \\ {x}^2+y^2={\left(3\right)}^2 \\ {x}^2+y^2=9 \end{gathered}$$