Question

Rectangular Equations to Polar Equations

Convert the equation to polar form.$x^2+y^2=9$

Short answer

The polar equation is$r^2=9$

Step-by-step solution

Step 1. Given information

An equation is given in a rectangular coordinate system as$x^2+y^2=9$

Step 2. Concept used

Replace the values in the formulas, do computations, and simplify the problem. For a precise response, consider a certain range, radius, and angle. Otherwise, the number of equations is limitless.

Step 3. Calculation

Formulae used,

$\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Substitute the values in the formulae,

$\begin{array}{l}\Rightarrow x^2+y^2=9\\ \text{Invalid <m:msup> element}\Rightarrow \text{Invalid <m:msup> element}+=9\\ \Rightarrow r^2{\cos }^2\theta +r^2{\sin }^2\theta =9\\ \Rightarrow r^2({\cos }^2\theta +{\sin }^2\theta )=9\\ \Rightarrow r^2=9\end{array}$