Question

Rectangular Equations to Polar Equations

Convert the equation to polar form. $x^2-y^2=1$

Short answer

The polar equation is $r^2=\sec 2\theta$

Step-by-step solution

Step1. Given information

An equation is given in rectangular coordinate system as$x^2-y^2=1$

Step2. Concept used

Substitute the values from the question into the formulas. If you simplify them, you'll get the solution.

Step3. Calculation

Formulae used,

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

Substitute the values in the formulae,

$\begin{array}{l}\Rightarrow x^2-y^2=1\\ \text{Invalid <m:msup> element}\Rightarrow \text{Invalid <m:msup> element}-=1\\ \Rightarrow r^2({\cos }^2\theta -{\sin }^2\theta )=1\\ \Rightarrow r^2\cos 2\theta =1\\ \Rightarrow r^2=\sec 2\theta \end{array}$